Phil Jagielka scored for the third game in a row to open the scoring before Sam Vokes levelled things up just minutes later with a penalty after being brought down by Joel Robles. However, a shot from Ross Barkley was deflected in via Ben Mee to restore the hosts lead before Romelu Lukaku netted for a ninth successive home game.
Hope despite defeat
Despite their abysmal record on the road this season, there were clear signs for optimism at the weekend. The Clarets were the better side for the first half-hour, with Michael Keane unlucky to see his header cleared off the line before Vokes was denied twice by Robles. A little more luck in front of goal and it would have been a very different game on Saturday afternoon.
Even when they fell behind to Jagielka's header, Burnley remained in confident mood. The away side responded quickly through Sam Vokes, who netted his 10th away goal of the season - five of which have come from the spot. The goal, while counting for little in the grand scheme of things, was indicative of the confidence and belief within Sean Dyche's side at Goodison Park.
For much of the second half, it looked as though the spoils would be shared. Heaten pulled off several good saves to keep Burnley in it, much to the frustration of Ronald Koeman's side. If Burnley can replicate the kind of performance they showed at the weekend, it will only be a matter of time before their fortunes on the road begin to change.
Defensive discipline lacking for Burnley
One thing that will have disappointed Sean Dyche will have been the way in which his side lost their defensive discipline in the second half. Having looked relatively comfortable at 1-1 with the prospect of a good away point on the cards, Burnley allowed Everton to score two quickfire goals and seal the victory.
The lack of composure away from home will be a worry for The Clarets for what remains of this season and it will surely be an area that they'll look to address in the summer transfer window, with their position in the top tier all but assured at this stage in the season.
On a different day, with the chances they had, Burnley could easily have taken away a valuable point against Everton. However, it will be back to the drawing board for the side, who are eight points above the drop, thanks to Swansea City and Hull City also suffering defeat.