Manchester City moved 17 points clear at the top of the Premier League table with a comfortable victory over Fulham.
The Cottagers, who defeated Liverpool last weekend, held their own during the first half but were three down by the hour mark after a disastrous start to the second period.
The Clarets' goals in their 2-1 success both came in the first half through excellent strikes from Chris Wood and Dwight McNeil.
Johann Berg Gudmundsson hit a post as Burnley looked to make it three before Dominic Calvert-Lewin pulled one back prior to half-time.
Both teams had chances in the second half, with Burnley hitting the woodwork again through Ben Mee, and it was the visitors who went home with the points to move seven points clear of the bottom three.
Chelsea extended their unbeaten Premier League run to 10 matches in an entertaining goalless draw at Leeds.
The Blues, who have not lost in 12 games in all competitions under manager Thomas Tuchel, were given a thorough workout by Leeds, who fully deserved their point.
Both sides struck the crossbar in a frenetic first half and both goalkeepers were forced into decisive saves.
It was also another clean sheet for Tuchel's side, who have conceded only two goals since he replaced Frank Lampard in January.
Luka Milivojevic's first-half penalty helped Crystal Palace take another step to safety with a 1-0 win over sinking West Brom.
Wilfried Zaha, who pre-match became the first Premier League player not to take the knee, won the spot-kick and Roy Hodgson saw his players keep a third clean sheet from their last four games to secure a vital victory.
It was a different story for the visitors, who lacked a cutting edge and look certain to be in the Sky Bet Championship next season.