Midfielder Saul Niguez opened the scoring in style with a 30-yard rocket into the top corner midway through the first half at Atletico's Wanda Metropolitano fortress.
The home side doubled their advantage two minutes into the second period when Antoine Griezmann's parried shot fell to Diego Costa to convert from close range.
Koke made Atletico's cushion to take to Russia even more commanding with a 90th-minute third, guiding a cross from Juanfran inside the post from 12 yards out.
Relive how the action unfolded in Spain with our minute-by-minute updates below.
5.00pmAfter defeat to Barcelona in a first-versus-second La Liga showdown on Sunday, the Europa League looks like Atletico's best chance of winning a trophy this season. Lokomotiv Moscow are their last-16 opponents, with Sports Mole bringing you the first leg from Spain tonight. Team news coming up...
5.06pmAtletico are without Jan Oblak tonight as he sits out because of a hand injury - which is a bit of a nuisance for a goalkeeper. One of the world's best stoppers is replaced by 22-year-old Argentine Axel Werner for his first-team debut.
5.08pmAntoine Griezmann and Diego Costa continue their burgeoning partnership up front with Kevin Gameiro, who scored in both legs of the previous round victory over Copenhagen, kept in reserve on the bench alongside Fernando Torres who is a serial substitute now in the twilight of his career.
5.10pmManager Diego Simeone makes three changes from the team which lost at the Camp Nou at the weekend, two in defence as Juanfran and Lucas Hernandez come in for Diego Godin and Sime Vrsaljko.
5.12pmElsewhere, experienced club captain Gabi Hernandez drops out for Angel Correa in an attacking change which suggests that Simeone would like to take full command of this tie in the home first leg.
5.14pmLokomotiv returned from their three-month winter domestic break with a 0-0 draw against fierce rivals Spartak Moscow on Sunday, and manager Yuri Semin obviously feels his players are well rested as he has only made one change, bringing in former Tottenham defender Vedran Corluka.
5.16pmTop scorer Jefferson Farfan, who has 12 goals for the season, is unavailable because of injury. The Peru international winger was once one of the hottest properties in Europe, during his days at Schalke, and although he never made it to the big time, he will be a big miss for Lokomotiv tonight.
5.18pmLeading the line for the Russians is Eder, who is not a prolific goalscorer but has one very famous strike to his name - the winner for Portugal in the final of the 2016 European Championships. The 30-year-old, on loan from Lille, has three goals in 15 appearances for Moscow this campaign.
5.20pmAnother name that you may recognise in the Lokomotiv XI is that of midfielder Manuel Fernandes, who had brief but promising spells at Portsmouth and Everton over a decade ago before forging a career for himself across Europe with Valencia, Besiktas and now Lokomotiv.
5.22pmAlongside the Portuguese in midfield are homegrown twins Aleksei and Anton Miranchuk, who have been described as 'the Russian De Boers', just now, by me, for the first time ever. The two are so close that they have even picked bizarre squad numbers next to each other - 59 and 60. Cute.
5.24pmAtletico's 1-0 defeat to Barca on Sunday has left them eight points adrift at the top of La Liga. While not an insurmountable deficit with 11 games to go, compared to Manchester City's 15-point lead for example, this is Barcelona we are talking about, so that match really was make or break.
5.26pmThat result ended an eight-match winning run in all competitions - their best sequence since November 2015 - and one which included two victories over Copenhagen in the last round as Atleti cruised to a 5-1 aggregate success over the Danish champions.
5.28pmLokomotiv also played Copenhagen twice in the process of topping their Europa League group. Compared to Atletico, they earned a less emphatic 2-1 advantage over the two fixtures and the scorer of both of those goals was Farfan, who of course is absent this evening.
5.30pmDespite their Camp Nou setback, Diego Simeone's side still hold a seven-point lead over their city rivals Real Madrid in second. They have to visit the Bernabeu a month today, so regaining momentum is crucial in the meantime, and that starts tonight.
5.32pmThat should not be difficult considering Atletico's impressive home form, which has seen them win their last five games at the Metropolitano without conceding. They are unbeaten at home in La Liga all season, but have lost three times in cup competitions.
5.34pmOf Madrid's last 11 competitive home matches, only once did they not win to nil, which illustrates just how solid they are defensively on their own patch. The exception was a 1-1 draw with Girona back in January when midfielder Portu broke their rearguard.
5.36pmWhile they may be devilishly effective, Atletico cannot claim to be as exciting as their neighbours, not that it will bother them. Ten of their previous 14 matches at their new stadium have seen less than three goals, although there has not been a 0-0 draw in sight.
5.38pmThere was a rare goal glut on Atletico's last match at the Metropolitano as they thrashed Leganes 4-0, with Antoine Griezmann bagging all four to take his tally to 20 for the season. He needs only six more to match his final haul for the 2016-17 campaign.
5.40pmGriezmann has struck up with an immediate relationship with Costa since the former Chelsea striker was cleared to play in January. Costa himself has five goals in 10 matches, and they appear to be the perfect balance of flair and brute force.
5.42pmAtletico's front two may not have it all their own way tonight, as Lokomotiv boast the second best defence in the Russian Premier League this season, conceding only 15 goals in 21 matches.
5.44pmThe Moscow outfit hold a seven-point lead over FC Krasnodar at the top of the table with nine games of the Russian season remaining. They have not won the title since 2004 and finished eighth last season, so manager Yuri Semin has overseen a big turnaround in the last 12 months.
It is the 70-year-old's fourth spell in charge, with his combined reigns totalling more than 25 years.
5.46pmLokomotiv are on a 10-game unbeaten run which stretches back to November, also only three of those matches have been in 2018. They do not seem to have lost any momentum following their winter break, but this Atletico side are a step up on anything they have faced this term.
5.48pmThat statement is supported by the odds to win this season's Europa League, with Atletico clear frontrunners and as short as 2/1 with some bookmakers. Borussia Dortmund and Arsenal are among the other favourites but Madrid's recent European pedigree makes them difficult to look past.
They did win the Europa League last time they dropped out of the Champions League, after all.
5.50pmSpeaking of Arsenal, Sports Mole also have live coverage of their clash with AC Milan at the San Siro, arguably one of the biggest matches of Arsene Wenger's tenure considering recent disappointments. Around 10 minutes until kickoff there, and here in the Spanish capital...
5.52pmLokomotiv overcame a difficult test in the form of Nice in the last 32, despite two goals from ex-Man City striker Mario Balotelli. Fernandez's hat-trick in France helped them to a 4-2 aggregate victory - only Aritz Aduriz of Bilbao has more Europa League goals than the Portuguese's six this term.
5.54pmAnother key player for the Russians is captain and midfielder Igor Denisov, who ranks fourth for completed passes in this season's competition. He is key to getting Lokomotiv ticking but tonight may be an occasion where they have much less of the ball than they are used to having.
5.56pmHEAD TO HEAD: These two teams have only met once before and it finished in a thrilling 3-3 draw. Sergio Aguero - you may have heard of him - scored twice for Atletico that day. Peter Odemwingie and Diniyar Bilyaletdinov and Diego Forlan were also on the scoresheet that day.
5.58pmPREDICTION: I can't see Lokomotiv, who are in the last 16 of this competition for the first time ever, causing Atletico's defence too many problems but they won't be pushovers either. The hosts should have enough to open up a pretty commanding 2-0 lead.
1 minKICKOFF: The Danish officials get the game underway, after a minute's applause in memory of ex-Fiorentina captain Davide Astori, whose funeral was held today after his sudden death.
3 minAtletico work the ball nicely down the right with Juanfran cutting a cross back for Griezmann, who could have struck it first time on his right foot but instead tried to set up something spectacular on his left, losing control of the ball.
5 minLokomotiv venture into the Atletico half for the first time of note but the bullish Gimenez is too strong for Eder, and the defenders ushers the ball back to the debutant Werner in goal.
7 minThe Miranchuk twins link up down the left but a hopeful shot on the turn from Aleksei is blocked by Gimenez.
9 minCorrea wastes a really good opening for Atletico, although one engineered by his own fancy footwork, by taking on a shot himself from 25 yards when Juanfran was free on the overlap.
11 minLucas Hernandez strides out from the Atletico defence with purpose, carrying the ball 50 yards without a challenge but a return pass from Saul was just too heavy for the Frenchman.
13 minA clever dummy from Griezmann earns Atletico a free kick which is aimed towards Costa, but Corluka climbs above the grizzly striker and gets good distance on his clearing header.
15 minThe visitors have struggled to get out of their own half in the opening quarter. Whether it is a deliberate tactic or has been forced on them by Atletico's front-foot start, they are penned back.
17 minAtletico are not a side which creates a load of chances so set pieces are very valuable to them. Griezmann lines up a 30-yard free kick but his effort strikes the top of the wall.
22 minAtletico take the lead and it is an absolute rocket from Saul! There is no movement ahead of the midfielder so he takes the shot on from 30 yards, catching Lokomotiv goalkeeper Guilherme by surprise and finding the top corner. It is his 10th European goal for Atletico and surely his best.
24 minEder tries to emulate Saul's long-distance strike but his shot from the left edge of the box is dragged wide. The rookie goalkeeper Werner is yet to be worked midway into his first half.
26 minThe right wing has been a good outlet for Atletico so far, with Correa and Juanfran both lively and Griezmann occasionally drifting over to offer support. Left-back Rybus could do with some help.
28 minSolomon Kvirkvelia dives in on Costa in the box, allowing the striker to easily escape his challenge and get to the byline, but his off-balance cross does not have the power to reach Griezmann.
30 minCHANCE! Guilherme breathes a huge sigh of relief after coming 30 yards off his line to unsuccessfully try to play the ball around Griezmann, only to gift possession to the Frenchman whose attempt to side foot the ball into the open goal from the left wing is just a few yards off.
33 minYELLOW! Aleksei Miranchuk is booked for diving while attempting to win a penalty under the challenge of Gimenez. It was a really good run from the Russian midfielder, and return pass from Maciej Rybus, before the 22-year-old threw himself to the floor.
35 minBoth sides have been sloppy in possession during the last five minutes or so and there was another nervy moment for Guilherme, whose pass played Kvirkvelia into trouble which he just about managed to escape from.
37 minGriezmann runs onto a back-heel from Koke and tries to pull a shot back towards the bottom corner from the edge of the box. It takes a deflection, making it easy pickings for Guilherme.
39 minThe ball is teed up for Anton Miranchuk to take on a shot from 25 yards out, but Eder is penalised for tugging the shirt of Lucas Hernandez during what looked like strong hold-up play.
41 minSaul slips a nice ball down the right channel for Correa to run onto but he is crowded out by two Lokomotiv defenders. More so than Griezmann or Costa, he has been Atleti's brightest spark.
43 minLokomotiv have all 11 men behind the ball now as they try to get through to half time with this slim deficit. If they took this scoreline back to Russia, you'd have thought they'd be pleased.
45 minGriezmann attempts to spread the play to the right where Atletico yet again had a 2-on-1 situation, but Rybus thwarts a potentially dangerous opening with a diving header to intercept.
6.50pmThe referee's whistle brings to an end what was a rather uneventful first half which was brought to life by one moment of magic from Saul, whose 30-yard stunner separates the sides at the break.
6.52pmIt has been a typically efficient display from Atletico so far, although Lokomotiv have had it quite easy for them by sitting 10 men behind the ball at times. The Russians have created one half-chance which fell to the wrong man - defender Vladislav Ignatyev - who sliced wide of the post.
6.54pmIt should really be 2-0 to the hosts after Lokomotiv goalkeeper Guilherme casually gave the ball away to Griezmann on the left byline, only for Atletico's top scorer to shoot wide of the open goal.
6.56pmUPDATE: Arsenal fans may finally have something to smile about tonight as their team lead 2-0 at half time against AC Milan at the San Siro - Aaron Ramsey adding to Mkhitaryan's opener.
7.00pmAtletico don't appear to be in any danger of losing this one either. The only question is whether they can extend their winning margin to take back to Russia next week because Lokomotiv are likely to sit back again to try to keep the deficit at one.
46 minKICKOFF: The action resumes with both sides unchanged from the first half...
47 minAtletico double their advantage within two minutes of the restart through Costa, who steers a rebound home after Guilherme had made a decent diving save to keep out Griezmann. The Frenchman was given loads of room at the back post and although he didn't make the visitors pay, Costa did.
49 minThat is Yuri Semin's half-time team talk out of the window! I wonder if Lokomotiv will change tact now and try to pinch an away goal, because otherwise they face a huge task in the second leg.
51 minLokomotiv right-back Vladislav Ignatyev is down receiving treatment having clashed knees with Saul. The Spaniard has escaped unscathed but Ignatyev is visibly in serious discomfort.
53 minSUBSTITUTION: The visitors waste no change in making the change as Russia Under-21 international Mikhail Lysov comes on in Ignatyev's place. He has gone to left-back and caused a bit of a reshuffle.
55 mnLuis knocks the ball down the line for Saul to chase down, and the midfielder hooks an excellent cross back into the danger zone which Corluka clears off the head of Costa. Saul's quality on the ball tonight has been excellent.
57 minSaul drifts over to the right wing now and exchanges a one-two with Griezmann, whose attempted cutback towards Costa is cut out by good defending from Nemanja Pejcinovic.
59 minPENALTY APPEAL! Costa wants a penalty after his shot is blocked by Corluka, who did turn away from the ball and stick is hands out to prevent it from going goalwards. The response from Costa is not as veciforous as perhaps it might have been had the scores still been goalless.
61 minAn incisive pass inside from the right from Juanfran opens up another shooting opportunity for Saul, but this time his radar is well off and his 25-yard strike flies high into the stands.
63 minMore authority shown this time from Guilherme as he comes off his line to claim a corner. The goalkeeper looks for options for a quick counter but non of his teammates shared his ambition.
65 minSHOT! Juanfran continues to be a good attacking outlet for the hosts and gets forward again here, with his low shot from the right edge of the box deflected into the side-netting.
67 minYELLOW! Correa is squeezed off the ball by two Lokomotiv bodies and lashes out in frustration with an ugly hack on Igor Denisov, earning a deserved caution for his troubles.
69 minSUBSTITUTION: Simeone takes the opportunity to spare Griezmann the final 20 minutes, with the visit of Celta Vigo on the horizion, bringing on Vitolo to play just in behind Costa.
71 minSUBSTITUTION: The visitors repond with a change of their own, bringing on Russia international midfielder Aleksandr Kolomeytsev for one of the twins - Anton Miranchuk.
73 minThomas Partey has had a quietly efficient game in the middle of the park. He doesn't have the same passing range as Koke or Saul but he knows his role and keeps things simple.
75 minSUBSTITUTION: Two more changes for Atletico, with preservation in mind. Kevin Gameiro and Fernando Torres are on for Costa and Correa, so a completely fresh attack now for the hosts.
78 minSAVE! Nearly 80 minutes in and Werner has had his first save to make. Substitute Lysov strikes the ball really cleanly from 30 yards but the Argentine holds the ball to his chest comfortably.
80 minGameiro releases Vitolo down the right channel but Corluka times his slide tackle perfectly to quell the threat.
82 minThe former Spurs and Man City defender required some treatment after possibly twinging his hamstring making that challenge. He is limping on for now but a substitution is being prepared.
84 minYELLOW! Saul's excellent night is somewhat soured with a needless yellow card late on. He had been turned by Denisov and the referee was quick to act on his pull of the shirt.
87 minDenisov gives Eder something to chase down but Lucas Hernandez comes across to cut off the Portuguese striker, who sends him tumbling into the advertising hoardings. The service up to the striker has been almost non-existent all night so you can understand his frustration.
89 minRight on cue, Rybus knocks a cross in from the rightt, 10 yards over the head of Eder at the back post.
90 minJuanfran's high pressing earns him the ball in the Lokomotiv half and he drives to the byline before pulling a cross back to Koke, who turns the ball inside the far post from 12 yards out.
90+2 minThat goal makes this scoreline more reflective of Atletico's dominance and almost certainly books them a ticket into the quarter-finals. Diego Simeone's men are going to take some stopping.
90+4 minFernandes swings a decent set piece into the box but Werner takes it cleanly.
7.52pmFULL TIME: ATLETICO MADRID 3-0 LOKOMOTIV MOSCOW
7.58pmAtletico run out commanding first-leg winners over Lokomotiv Moscow and open up what is surely an insurmountable lead heading to Russia next week. Saul started things off with a beauty and goals at each end of the second half from Diego Costa and Koke leave the Spaniards in complete control.
8.00pmYou can read our match report on another Atletico home win here, and that is it from me. Thanks for joining Sports Mole this evening and please rejoin us for extensive coverage of this weekend's Premier League games, starting with Liverpool vs. Manchester United. Until then, goodbye!