The visitors took the lead in the first half through Cenk Tosun, whose firm header saw him open his account for the club in just his third start since his £27m January arrival.
However, second-half goals from Ashley Barnes and Chris Wood saw Burnley turn the game around to end a 12-match winless streak, while Everton's misery was compounded late on when Ashley Williams was shown a straight red card.
Find out how all of the action unfolded courtesy of Sports Mole's minute-by-minute updates below.
Only two places and three points separate these two sides in the top half of the table and both should be safe from being dragged into a very busy relegation battle, but neither come into this match in particularly good form.
We will take a closer look at that in a short while, but first let's check out the team news...
Well, the headlines news comes from the Everton camp so we'll start with the visitors as Sam Allardyce drops Wayne Rooney to the bench for this one.
The former Manchester United man is replaced in the starting lineup by Dominic Calvert-Lewin as Allardyce switches up his formation once again with what looks more like a 4-4-2 formation this afternoon.
There is another change in the attacking part of the field, though, with Cenk Tosun being handed a rare start in place of Oumar Niasse. The Turkish striker has started just twice for Everton since his £27m move from Besiktas in January and is yet to score a goal for the Toffees, but he is given another chance today.
It is an otherwise unchanged back four in terms of starters, with Williams and Keane in the middle and Martina on the left, but there is a notable inclusion on the bench as Leighton Baines continues his recovery from a long-term injury of his own.
There is some good attacking talent on the bench too should Plan A not be working for the Toffees, with Bolasie joining Niasse and Rooney among the substitutes.
Tarkowski played the entirety of a behind-closed-doors friendly against Preston on Tuesday and comes straight back into the starting lineup today as Burnley are finally able to once again field what is arguably their strongest back four.
Nick Pope once again gets the gloves behind them and has been in fine form this season since replacing Heaton, so much so that it will be interesting to see who is the number one once Heaton finally returns - something which is not too far away now.
Alongside him in the middle of the park will be Westwood and Hendrick, but the main threat could come from Gudmundsson, who has two goals and five assists to his name in the top flight this season.
The fact that Barnes still only has four goals for the campaign is alarming, though, and betrays Burnley's biggest problem of scoring goals.
It is, of course, mainly down to their style of play, but only Swansea City have scored fewer goals in the entire league this season, with the Clarets finding the back of the net just 22 times in their 28 appearances.
Fans will even accept such a measly goal tally if it translates into a seventh-placed finish, with the Clarets now only one win away from the magic 40-point mark despite their recent dip in form.
Dyche's side were within touching distance of their first win since mid-December last weekend, but a last-gasp Gabbiadini goal denied them victory at the death against Southampton. Even so, Burnley are still six points and five places better off than at the same stage of last season, and there is no doubt that the fans, players and manager would have taken their current position at this stage if it was offered to them at the start of the season.
The Clarets have only ever been on a longer Premier League winless run once - a 12-game streak which ended in January 2010 - while in all competitions they are on their longest winless run since one of 19 games ended in March 2007.
Burnley have not gone six home games without a win since October 2014, although it should be noted that they have hosted Tottenham, Liverpool, Manchester United and Manchester City in that time, drawing with the latter and following that up with the stalemate against Southampton.
Indeed, the Clarets have scored more than twice in any of their last 22 Premier League home games, stretching back to December 2016, so do not expect a goalfest this afternoon.
It just so happens that they are coming up against a team which has won the lowest percentage of their points away from home this season, though, with only eight of Everton's 34 points - that's just 24% - coming on their travels.
However, one stat he will be keen to get rid of during his time in charge is that his side have failed to win any of the 53 Premier League matches in which they have conceded the opening goal under Dyche, drawing 11 of those and losing 42. The first goal could be crucial today, then.
Unlike Burnley, though, Everton have been poor at the back as well, with only three teams conceding more goals in the entire league. Sam Allardyce has a reputation for tightening things up at the back, but he has chopped and changed his defence so far and still seems to be unsure on his best unit.
Allardyce does have a contract which extends beyond the end of the current campaign, but his side's recent results - and the playing style which has been implemented by Allardyce - have been criticised. Marco Silva is understood to be the favourite to replace him.
Both of those wins have come in Everton's last four games, though, and in the Premier League their record over the past five games is evenly stacked at two wins, two defeats and a draw - having lost three league games in a row around the turn of the year.
The Toffees are only two wins away from the 40-point mark, but the fact that that is their target at this stage of the season goes to show what a disappointing campaign it has been. Everton had hopes of challenging the top six this term, but they are a whopping 13 points worse off than at the same stage of last season.
That includes four away defeats in the Premier League, and another this afternoon would see them fall to five on the bounce for the first time since January 2015. their poor away form stretches back further than just this latest run, though, having now won only one of their last 22 league games on their travels, losing 12 of those.
It is their record on their travels which has really cost them this season as they would sit seventh if only home form counted, whereas using only away records Everton would be in the relegation zone with eight points and eight defeats on the road.
Neither of these sides are in particularly good form, and the home-away records are both so poor that they could end up cancelling each other out. I am not expecting goals galore, but I'm going to plump for a score draw.
SPORTS MOLE SAYS: Burnley 1-1 Everton
Burnley have won two of their three Premier League home games against Everton too, including a 2-1 triumph in the corresponding fixture last season when Arfield scored a late winner after Bolasie had cancelled out a Vokes opener.
Another win for Sean Dyche's side today will see them complete the league double over Everton for the first time since the 1959-50 campaign, when Burnley went on to win the top-flight title.
Indeed, it has been fairly even between these two sides during the Premier League era, with Everton winning four times and Burnley three. However, Sam Allardyce has only ever lost two of his 14 league meetings with Burnley as a manager, and is unbeaten in six previous visits to Turf Moor.
BURNLEY STARTING XI: Pope; Lowton, Tarkowski, Mee, Ward; Lennon, Cork, Hendrick, Westwood, Gudmundsson; Barnes
EVERTON STARTING XI: Pickford; Coleman, Williams, Keane, Martina; Gueye, Davies, Sigurdsson, Walcott; Calvert-Lewin, Tosun
Walcott drives down the right flank before playing a cross into the middle which Coleman flicks on well. That takes the ball to Tosun, who plants a firm header into the bottom corner past a helpless Pope.
WATCH: Cenk Tosun gets nods Everton ahead after some good work from Walcott and Coleman!— Sky Sports PL (@SkySportsPL) March 3, 2018
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Pickford keeps his side in the lead with this wonderful save, with Gareth Southgate watching on...👀— Sky Sports PL (@SkySportsPL) March 3, 2018
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It is Everton who take the lead into half time, but Burnley have created plenty of chances themselves and it is still all to play for in the coming 45 minutes.
It was a goal which came against the run of play, but Everton had threatened before that. Coleman got a crucial flick on to help Walcott's cross into the path of Tosun, who made no mistake with a confident finish.
Aside from that there have been other chances for Tosun and Walcott, but Everton's main threat has come on the counter-attack, with Burnley looking the more dangerous of the two teams in general play.
Barnes has been a real nuisance for Burnley all game so far, and the Clarets have also seen the likes of Gudmundsson, Cork and Lennon all miss chances.
It is a great pass from Lowton down the channel which releases the striker, but Pickford could perhaps come to meet it. Once Barnes does eventually latch on to the pass he is virtually in the six-yard box, and he is able to slam his finish home at the near post.
Ashley Barnes' equaliser means that Everton have now conceded 30+ away PL goals in a season for the 1st time since 2004-05 pic.twitter.com/XGwHdG4P1O— Sky Sports Statto (@SkySportsStatto) March 3, 2018
The defending from Williams and Keane is poor again - they have been dreadful today - as Wood loses Williams before climbing above Keane in the area and thumping a close-range header past PIckford.
Barnes had terrorised WIlliams and Keane all game up until that point, and he and Wood got the goals which saw the Clarets turn the game around in the second half, having gone into the break behind courtesy of Tosun's first Everton goal.
Thank you very much for joining Sports Mole for today's early Premier League kickoff as Burnley come from behind to beat 10-man Everton, reaching the 40-point mark in the process. I will leave you with our match report, and be sure to stick around for reaction too. We also have coverage of the 3pm kickoffs live on site now, so check them out for more live action!
From me, though, it is goodbye for now!