Maxwel Cornet scored in the final minutes to help Burnley secure a vital 3-2 win over Everton at Turf Moor.
The Clarets are now just one point behind Frank Lampard's side, who will rue Jordan Pickford's mistakes after they went ahead in the match.
Nathan Collins scored at the back post from a corner to give the lead to Burnley after 12 minutes.
The advantage didn't last long as Richarlison stroked home a penalty six minutes later following a foul from Ashley Westwood on Anthony Gordon.
The Brazilian scored another penalty before half-time after Mike Dean initially denied a spot-kick following Aaron Lennon's trip on Vitaliy Mykolenko.
Dean was advised by the video assistant referee to review it on the monitor and then overturned his decision.
You just knew Sean Dyche's side wouldn't lie down and they eventually equalised after 57 minutes when Charlie Taylor's cross was met by Jay Rodriguez.
Everton created the better chances of the second-half, but it was Cornet who scored the winning goal with five minutes remaining.
Speaking after the game, Lampard warned his players to keep despite the outside pressure.
He told Sky Sports (via BBC): "We have to not get too caught up in the words. We have to keep working and preparing and give everything. Because if we do make mistakes like we did tonight we better be ready to fight. That's what it is.
"Players don't need to listen, or read, or get involved in anything other than turning up tomorrow and getting right for Saturday and trying to get the right results to keep us in this league.
"The only thing we can do is control what we can. Which is to work and fight and get the results."
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