Substitute Robin Gosens killed off any hopes of a comeback from David Unsworth's side with a left-footed volley into the bottom corner via the post on 86 minutes.
There was still time for former Cardiff City striker Andreas Cornelius to score twice and do further damage to Unsworth's hopes of landing the permanent manager's job.
Relive how the action unfolded on Merseyside with Sports Mole's minute-by-minute updates.
7.00pmThe red half of Merseyside has already thrown up a European thriller this week and now it is the turn of the blue half as Everton host Atalanta at Goodison Park in the final home game of their miserable Europa League campaign. David Unsworth remains in caretaker charge, so what team has he gone with?
7.06pmUnsworth promised a strong side but he has made nine changes from Saturday's 2-2 draw with Crystal Palace. Only Jonjoe Kenny and Michael Keane retain their places, and there is no Oumar Niasse in the squad despite his two-match ban for diving only applying to domestic competition.
7.08pmJordan Pickford gets his first rest of the season as Joel Robles deputises in goal. There is also another start for 19-year-old Beni Baningime alongside fellow academy graduate Tom Davies in a youthful midfield. Wayne Rooney captains the team having been an unused substitute at Selhurst Park.
7.10pmNiasse's controversial ban - more on that later - gives Sandro Ramirez a chance to impress. The 22-year-old is yet to score for the Toffees, and this is his first start since Apollon Limassol away in September.
7.12pmCuco Martina, whose went off with a nasty head injury on his last appearance against Lyon, is asked to do a job at left-back to give Leighton Baines a night off. Phil Jagielka, Gylfi Sigurdsson, Aaron Lennon and the suspended Morgan Schneiderlin are also left out of the squad entirely.
7.14pmOpportunities have been hard to come by for Nikola Vlasic since the sacking of Ronald Koeman. The young Croatian midfielder is on the bench alongside the likes of Ademola Lookman and Dominic Calvert-Lewin - showing the progress of youth as the Dutchman's one positive legacy.
7.16pmAtalanta rolled over Everton in the reverse fixture in Italy, winning 3-0 in September and all three of the goalscorers from that night start tonight - Andrea Masiello, Bryan Cristante and captain Alejandro Gomez.
7.18pmThere will be a couple of familiar names to avid Premier League historians in the Atalanta lineup. Ex-Middlesbrough midfielder Marten de Roon starts, while Cardiff City flop Andreas Cornelius only makes the bench.
7.20pmAlso among the visiting substitute is Josip Ilicic, a proven Serie A marksman over the years and is Atalanta's top scorer in the competition this season with two goals. Not a bad option to turn to.
7.22pmAtalanta are sitting pretty at the top of Group E having won two and drawn two of their Europa League games this season. Their progress to the last 32 will be secured tonight if Apollon Limassol drop points at Lyon.
7.24pmThe Toffees are bottom of Group E having failed to win any of their four matches so far. Their European campaign has proven to accentuate Everton's problems rather than be a distraction from poor league form.
7.26pmOne of the only positives from Everton's European expedition so far is that it has given several youngsters a platform to break through Beni Baningime is one of the youngsters who Unsworth knows well from his time in the academy and will be hoping to impress again this evening.
7.28pmUnsworth has continued to put his faith in youth as he auditions for the manager's job on a permanent basis. Marco Silva, Sam Allardyce, Louis van Gaal and Ralf Rangnick all appear to be out of contention, so Unsworth's fate is very much in his own hands and a good performance tonight will help.
7.30pmJudging from his pre-match comments surrounding future transfer activity, Unsworth is planning to be in charge come January.
BBC Sport quote him as saying: "Conversations have already taken place as regards areas we need improving, or recruitment in January, and they will continue. I am in communication with every department. That won't change day to day, week to week, depending on how long I am in the job, until somebody else takes this seat."
7.32pmRegardless of who the manager is, a striker will surely be top of Everton's January wishlist, and the Toffees have been left even shorter up front following the suspension of Niasse, who became the first Premier League player to be retrospectively charged for simulation this week.
7.34pmUnsworth was not happy that an example was made out of Niasse when others have got away with similar offences free of punishment, and thinks the FA will now have to hand out a lot of bans.
He told reporters: "I think these people [the FA] will be very busy. It's a dangerous precedent that could be set if decisions are given against you which are debatable. "I think anywhere on the field it's a foul. He [Niasse] was shocked and I was shocked [by the charge]."
7.36pmIn more positive news for Everton, they have signed a 200-year agreement to lease land on Bramley Moore Dock, near the centre of Liverpool with a view to constructing a new 50,000-seater stadium on the site. Planning permission and funding is now needed before work can be started.
7.38pmGoodison Park still has a few famous nights up its sleeve yet, although they have been non-existent this season. Defeat tonight would see Everton lose consecutive home European matches for only the second time - previously versus Benfica and BATE Borisov in the 2009-10 Europa League.
7.40pmThe rest of the Premier League is thriving on the continent, but a loss this evening would see Everton match Blackburn Rovers from the 1995-96 Champions League as the only English clubs to have as few as one point from their opening five group games in either the Champions League or Europa League.
7.42pmAtalanta are unbeaten in Europe this season but their away record over a longer period is encouraging for Everton. The Italians have only won one of their 12 away European games in their history - drawing five and losing six - with Turkish outfit Fenerbahce that solitary scalp in the 1990-91 UEFA Cup.
7.44pmJust over 20 minutes until kickoff on Merseyside. We are not expecting a full house considering that very little is at stake in this game, and also Everton's recent form - one win in 10 in all competitions.
7.46pmAtalanta have not been at their best in recent weeks either, failing to win any of their last four matches and slipping to 12th in the Serie A table. They were never expected to match their tremendous fourth-place finish of last season, but a lack of consistency has held them back this term.
7.48pmAtalanta fans have been enjoying themselves in the city of Liverpool today...
7.50pmThe Toffees have conceded 10 goals in their four Europa League games this season. Prior to kickoff tonight, only Vardar (17) and Austria Vienna (11) had shipped more which is shocking to say that Everton were tipped to go far in the competition in pre-season. A lot has gone wrong since then.
7.52pmEverything that has gone wrong for Everton so far this season started with a disastrous transfer window. Davy Klaassen has probably been the most disappointing of all of the arrivals so far and will be looking to take his chance tonight to kickstart his Everton career.
7.54pmRESULT: Good news Everton, however badly it goes tonight, Arsenal will make the back pages tomorrow having slumped to a 1-0 defeat to Bundesliga strugglers Koln in Germany. That feel-good factor from the North London derby lasted all of five days, then...
7.56pmIt has been a disappointing week for this man, who will be hoping for an Everton win as a pick me up...
7.58pmPREDICTION: Atalanta are a decent side but very poor travellers and I expect Everton will pick up a morale-boosting win this evening. I'm going for 2-0 with a goal for either Sandro or Klaassen.
8.00pmThe players make their way out onto the field and there are plenty of empty seats as anticipated. The Atalanta supporters are in good voice though and will be hoping for a repeat of September's triumph.
8.02pmUnsworth does not strike me as the type of manager to allow standards to drop, even when there is little at stake. He will be expecting his Everton players to put on a performance as they desperately seek some momentum heading into this weekend's Premier League match with Southampton.
1 minKICKOFF! The action gets underway on the whistle of the Danish referee...
2 minAn early sighter for Klaassen who hits over the crossbar on the half-volley from 20 yards out. The Dutchman needs something like that to come off for him to give him some much-needed confidence.
4 minRooney is released down the right and crosses into a great area for Sandro. Atalanta goalkeeper Etrit Berisha is off his line well to intercept, but does take a knock on his head from the Spaniard for his troubles.
6 minBerisha's blow required some medical attention which brought the game to a halt for a couple of minutes. Thankfully it looks as though the Albanian will be able to shake it off and carry on.
8 minKlaassen's through-ball to Sandro is a little overhit and forces the Spaniard too wide for him to make anything of it. Everton have started promisingly though while their visitors are yet to settle.
10 minAtalanta get their first corner of the game but Ashley Williams is on hand to head it away at the near post. The Welshman has let Everton down this season and needs to rediscover his form.
12 minOut of nowhere, Atalanta lead through their on-loan Benfica midfielder Cristante. Timothy Castagne gets down the right on the overlap, not tracked by Klaassen, skips past Keane will ease and cuts the ball pack into a crowd of bodies from which Cristante taps into the net.
14 minAtalanta had started quite slowly but will be very encouraged by the way that Everton's defence is crumbling every time they attack. The Toffees don't look organised and look especially vulnerable down the left channel between Martina and Keane.
16 minKeane sniffs out a long ball intended for Italy u21 international Andrea Petagna, but then hacks a wild clearance into the stands. That just goes to show the lack of confidence he is playing with.
18 minThe Italians work it nicely around the edge of the box but Petagna and Castagne are not on the same wavelength as the striker tried to release his wing-back with an acute through-pass.
20 minAtalanta have grabbed full control of this game now. Gomez drops the shoulder to get away from Davies and the Everton teenager has to foul the visiting captain 25 yards out from goal. The free kick is drilled low but Robles, making his first start of the season, gathers into his body.
22 minRooney is playing as a No.10 tonight behind Ramirez but is spending a lot of time drifting over to the right flank. With Mirallas out there as well it seems that is an area Unsworth has targeted.
24 minKenny knocks a cross deep but both Rooney and Klaassen are outjumped by Jose Luis Palomino and the danger is cleared. Everton aren't going to get much success playing that way.
27 minStrong tackle from Kenny on Hans Hateboer, who had skipped away from Sandro. With Seamus Coleman still at least a month away, the young full-back looks poised for a long run in the team.
29 minYou can tell this is an Everton team which is just not on the same page. Martina and Klaassen just bumped into each other, and a Rooney and Mirallas mix-up brings an attack to a premature end.
31 minCHANCE! Sandro misses a great chance to open his Everton account, snatching at a rebound 12 yards out and blazing over the crossbar. Mirallas perhaps should have scored himself but took a touch too many under pressure from Masiello and narrowed the angle too much.
33 minKeane and Williams both go to attack Rooney's corner and get in each other way. If either of the defenders had a clear run at that, they had an unmarked header 12 yards from goal.
35 minPetagna is an imposing unit leading the Atalanta line and his hold-up play has been very good so far. He wriggles away from Martina and takes a shot on himself, but it is weak and wide.
37 minKlaassen barges into Petagna to concede a free kick midway into the Everton half. Freuler and Gomez work a quick one but the delivery from the skipper is over his teammates in the box.
38 minOFF THE LINE! Outstanding defending from Rafael Toloi who spectacularly heads off the line. Sandro's back-heel released Martina to the byline and his cross, just above Rooney, is picked up by Davies whose shot has Berisha beaten but is brilliantly cleared by the retreating Toloi.
40 minBeningime makes a crucial tackle from behind on Cristante after the goalscorer skipped away from Williams and threatened to advance into the box. It was from behind but perfectly timed.
42 minEverton enjoyed a good five minute spell during which they created a couple of chances, but Atalanta have regained command of possession and are passing the ball around nicely.
44 minYELLOW! Williams is the first player into the referee's book this evening. Beningime showed how to tackle from behind a few minutes ago but this is horrible from the Welshman, late and he catches Masiello on the Achilles.
45+1 minMasiello hobbles off to receive further treatment and he looks in serious discomfort. The physio gives Atalanta coach Gian Piero Gasperini the universal 'let's give it until half time signal.
45+2 minSHOT! Back on the pitch, Masiello's clearing header drops to Mirallas who strikes first time with his right foot. He doesn't hit it that cleanly, but it is on target and Berisha has to make a low save.
8.56pmMore European misery for Everton so far then. They have had a couple of good chances to equalise since Bryan Cristante's 12th-minute opener, but trail 1-0 at the break at a half-empty Goodison Park.
8.58pmIt doesn't look as though it is going to happen for Sandro at Everton, with the Spanish striker squandering his side's best chance with a wild shot from 12 yards. Klaassen hasn't been up to much either, although stuck out on the left flank he has not been as involved as he'd like to have been.
9.00pmDavies and Beningime have been Everton's best players in the middle of the park, and the former would have equalised were it not for an unbelievable headed clearance on the line from Toloi.
9.02pmAtalanta started slowly but have been pretty good since taking the lead, albeit with a helping hand from an Everton defence which has been too easy to get at, especially down the flanks. On this evidence, it is little surprise to learn that Everton have conceded 20 goals in their last eight matches.
9.04pmLATEST: A point tonight would be enough for Atalanta to qualify, but regardless their progress to the last 32 looks in the bag with Lyon leading 2-0 against Limassol. If the Italians can close out this victory, it will set up a winner-take-all clash with Lyon for top spot in Group E.
9.06pmBENCH WATCH: I'm sure Everton fans would like to see Nikola Vlasic in the second half. The 20-year-old was in the team and doing okay before Koeman's sacking and would be more effective than Klaassen in a wide role.
46 minKICKOFF: Everton resume the action with both sides unchanged. Masiello is going to try to run off that knock that he sustained from the Williams challenge late on in the first half.
48 minPENALTY SAVED! Robles makes a fantastic double save to prevent Everton from making the worst possible start to the second half. Williams was adjudged, harshly it seems, to have brought down Cristante in the box. Robles saves the penalty to his right and then reacts brilliantly to block the follow up. A scramble ensues but Everton somehow clear the ball without conceding.
50 minSAVE! Gomez wants revenge on Robles and creates space for a shot 20 yards from goal that the stand-in Everton keeper gets down to, pushing it away from the bottom corner.
52 minSAVE! Everton are living on the edge here. Williams accidentally flicks on an Atalanta corner at the near post and Robles shows great reflexes to save right underneath his own crossbar. Cristante heads the follow-up goalwards but Kenny is on hand to hook off the line.
54 minThe visitors have started this half on a mission to kill the game, and would have were it not for Robles. It is ironic that one of the few Everton players making a case for themselves is the one player who certainly won't feature against Southampton this weekend.
56 minUnsworth has switched to a 4-4-2 diamond in this second half, with Mirallas alongside Sandro and Rooney in behind. The way that Atalanta have played since the break means that Everton's two strikers have not had the chance to get at the visiting defence yet.
58 minWhat has happened to the Michael Keane of last season? The defender is furious for not getting a foul against Hateboer, but really it was just shoulder to shoulder and the former Burnley man was nowhere near strong enough. Hateboer moves in on goal but rifles high and wide.
60 minAtalanta have taken it up a notch in this second half and now look a physical, technical side. In their search for a new manager, Everton could do worse than Gian Piero Gasperini if his team's play like this.
61 minSUBSTITUTION: Masiello has not looked comfortable since his injury and now comes off for Mattia Caldara, who was bought by Juventus for €15m in the summer and loaned back to Atalanta.
62 minSUBSTITUTION: Klaassen gets a pat on the head from Unsworth but won't have done much to impress Everton's caretaker boss tonight. Now Vlasic will hope to take his opportunity.
64 minAtalanta get the second goal that their dominance deserves, and it is another for Cristante, who gets in between Williams and Davies and glances a header in at the near post. Not much Robles can do about that one through a crowded box.
66 minGood pressing from Vlasic as he forces Gomez back into his own corner to a round of applause from the Everton supporters. It is the Atalanta fans who are rocking though, and who can blame them?
67 minYELLOW! Martina follows Williams into the book for dragging down Castagne by the back of his neck.
68 minKenny's cushions a volleyed cross into a really dangerous area but Everton have nobody in the box. Groans travel across Goodison, with No.10s Sandro, Rooney and Vlasic all on the edge of the area.
69 minSUBSTITUTIONS: Bootle-born 18-year-old Morgan Feeney will have dreamt of his Everton debut since he was a young boy, but probably never invisaged it in this situation. The teenage defender is on for Kenny, while Atalanta swap Robin Gosens for Hateboer at left-wing back.
71 minEverton pull one back and Sandro has his first goal in Everton colours! Rooney releases Mirallas down the right and the Belgian cuts the ball back for Sandro, whose first touch is a little behind him and makes the finish across Berisha and into the bottom corner from 15 yards all the more impressive.
73 minEverton have come from two down to beat Watford and pegged Crystal Palace back twice in their last two matches? Could another comeback be on the cards here? That goal has given them a chance.
76 minYELLOW! Davies is the third Everton man into the book after clipping Freuler with a late challenge.
77 minGomez drifts in from the left flank and rolls the ball into the feet of Petagna, who somehow goes unchallenged as he spins on goal and shoots, fortunately for the Everto defence, straight at Robles.
79 minSUBSTITUTION: Final change from Unsworth as Dominic Calvert-Lewin, who has five goals this season, replaces Mirallas up front.
81 minThe visitors have responded well to Sandro's goal, halting the Everton momentum and creating a couple of chances of their own. I'd be surprised if the Toffees don't come at them in the last 10 though.
83 minSUBSTITUTION: Ex-Cardiff City striker Cornelius, who never scored for the Bluebirds, gets the last few minutes at Goodison Park as goalscorer Cristante leaves to a great ovation from the away fans.
85 minHere comes that Everton rally I predicted. Sandro strikes a clean half-volley which Berisha parries, and Keane then hits the crossbar with a powerful header, only to be pulled up for a push on Palomino.
88 minThis just got ugly real fast, with Cardiff flop Cornelius scoring a fourth. Everton debutant Feeney drops too deep and plays the striker onside, and he cuts back onto his right foot and shoots through Robles. Things are going from bad to worse for the Toffees, and their caretaker manager.
90 minCaptain Gomez threatens a fifth for Atalanta with a shot which he drags wide from 22 yards out. Meanwhile Calvert-Lewin is shown a yellow card following a frustrating challenge on Gosens.
90+2 minThis is humilating now for Everton as Cornelius rises to head home a corner for his second and a fifth for Atalanta. A defeat of this magnitude must signal the end of Unsworth's chances of getting the job.
10.03pmThat escalated quickly! Everton were pushing for an admirable come-from-behind draw with five minutes to go, and suddenly found themselves on the end of a 5-1 hiding to a side that had not won away all season. Absolutely shambolic defending from the Toffees - a new low in a very low season.