Kevin Mirallas gave Everton the lead just before the half-hour mark and when Ashley Barnes was sent off just before half-time for a second bookable offence there was no way back for the visitors.
A win would have lifted Sean Dyche’s men out of the drop zone but instead they are now bottom of the Premier League with just five games left to play.
For Everton, the season is ending on something of a high after their Europa League travails and a fourth win in five games rarely looked in doubt as they troubled Burnley from the outset.
Indeed, Roberto Martinez’s men should have gone ahead from the penalty spot inside the opening 10 minutes when Aaron Lennon was brought down by David Jones right on the edge of the box.
Long-time penalty taker Leighton Baines was on the pitch but instead it was Barkley who took responsibility only to see his effort saved by goalkeeper Tom Heaton away to his right.
Everton did not have long to wait for the breakthrough, however, when Mirallas capitalised on good work from James McCarthy down the right flank to give the home side the lead.
Mirallas met McCarthy’s cut-back and while his first attempt got stuck under his feet, he was able to prod it past Heaton at the second time of asking to score his sixth Premier League goal of the season.
Jones squandered a good chance to equalise soon after with Burnley well in the contest for the remainder of the half, but Barnes’ red card ensured the opening 45 minutes ended on a sour note.
Barnes has committed more fouls than anyone in the Premier League this season and was punished for a foul on Seamus Coleman having already gone to ground once when lunging in on McCarthy.
Mirallas was lucky not to join Barnes when he caught George Boyd with his studs early in the second half but escaped with only a yellow card from referee Mike Jones.
Everton dominated possession as would be expected but were a little wasteful in front of goal, most notably when McCarthy passed the ball just wide of the post when well placed.
Gareth Barry might have ended all hope of an equaliser had he finished when unmarked at the far post but instead it was the 10 men who forced an anxious finish for Martinez’s men.
Danny Ings, without a goal in eight games now, might even have earned his side a point had he hit the target with a free header from close range.
But the chance was spurned and Everton claimed the three points to move within two points of the top half of the league table. Burnley will just be hoping to be in that Premier League next season.
Soccer Saturday verdict – Paul Merson
“Burnley will feel hard done by. Ashley Barnes has got two yellows for his enthusiasm. The second one did not deserve it. They also should have had a penalty. It was handball by John Stones. Stonewall penalty.
“Then, Mirallas goes into a tackle on Boyd’s shin. When the referee sees it back he will be disappointed not to have given a red. Aaron Lennon was excellent all game. A real threat.”
Everton: Howard (6), Coleman (7), Stones (7), Jagielka (7), Baines (7), McCarthy (7), Barry (6), Lennon (7), Barkley (6), Mirallas (6), Kone (5)
Subs: Lukaku (6), Naismith (6), Besic (6)
Burnley: Heaton (7), Trippier (6), Duff (7), Shackell (6), Mee (6), Boyd (7), Arfield (6), Jones (5), Barnes (5), Ings (7), Vokes (6)
Subs: Jutkiewicz (6), Wallace (6), Taylor (6)
Man of the Match: James McCarthy