An own goal from Kevin Long and a Victor Moses strike was enough to hand Chelsea victory.
Chelsea kept alive its slim chance of sneaking into next season's Champions League with a 2-1 win at Burnley Thursday.
An own goal from Kevin Long and a Victor Moses strike was enough to hand Chelsea victory. Ashley Barnes was on target for Burnley.
It is the first time Chelsea has won back-to-back league matches since December and saw Antonio Conte's men move within five points of fourth-place Tottenham with four matches remaining. The top four in the Premier League qualify for Europe's premier club competition.
"If we think about the past, for sure we have missed great chances to stay closer to them," Conte said. "The only way to go to keep up is to try to get three points in every game from now until the end."
Chelsea made six changes at high-flying Burnley, with Olivier Giroud being rewarded for his double against Southampton on Saturday with a starting place.
Sean Dyche named an unchanged side as Burnley looked to move above sixth-place Arsenal with a sixth straight win.
"There are certainly no disappointments," Dyche said. "Our judgment really is that we're playing a top side and I think we're getting closer.
"We've still got loads of work to do but the gap has got closer over the last three seasons."
Chelsea dominated and took the lead in the 20th minute when Long deflected the ball into his own net after good work on the right by Moses.
Alvaro Morata has had a poor season since his summer move from Real Madrid and he should have doubled Chelsea's lead in the second half but somehow fired wide when clean through against goalkeeper Nick Pope.
Burnley leveled in the 64th minute in fortunate circumstances as Johann Berg Gudmundsson's effort from the edge of the area was deflected into the bottom corner by Barnes.
It took Chelsea five minutes to restore its lead with Moses left unmarked to fire in Emerson's cross from the left.
Morata was replaced by Eden Hazard moments later and reacted angrily to his exit.
"Alvaro must be angry because when you have a chance to score, you have to score, especially for a striker," Conte said.
