Burnley looked set to claim a point thanks to Ashley Barnes' lucky equaliser, but Moses came up with the decisive goal in the 69th minute to boost his side's slim hopes of UEFA Champions League qualification.

Winning at Turf Moor on Thursday moves Chelsea within five points of London rival Tottenham in the battle for a top-four finish, Conte's decision to leave Hazard and Willian on the bench at kick-off ahead of Monday's (AEST) clash with Southampton at Wembley justified by the result.

Kevin Long's own goal gave Chelsea the lead, the defender bundling a Moses centre in after Gary Cahill's long pass sent the wing-back behind the Clarets' back line.

Barnes inadvertently deflected in Johann Gudmundsson's shot past Thibaut Courtois for his eighth Premier League goal of the season but Sean Dyche's side saw their five-game winning streak end thanks a rapid response.

Moses was a threat down the right all game and the wing-back thumped in a low drive that beat birthday boy Nick Pope at his near post to claim all three points for the visitors.

Conte paired Olivier Giroud and Morata in attack and the Spain forward had the game's first chance from a tight angle, Pope saving with his right boot.

Pope was helpless as Chelsea took the lead in the 20th minute, though, the goalkeeper touching on a Moses cross that deflected into his net off defender Long.

Burnley was struggling to cope with Chelsea's front two and Pope had to be quick off his line in the 32nd minute to deny Morata after the striker was played into the box by Giroud.

The visitor was given a golden chance to double its lead after the break when N'Golo Kante intercepted a poor Matt Lowton pass and sent Morata clear, but despite Pope's hesitance the striker somehow fired wide of the post.

Moses burst away from a static Burnley midfield to get into the box but fired straight at Pope, who was again keeping club captain Tom Heaton on the bench.

The Clarets promptly levelled with their first shot on target of the match in the 64th minute, although there was a huge slice of luck involved.

Gudmundsson cut inside from the right and fired at goal, his strike taking a massive deflection off Barnes - onside despite Chelsea protests - to wrongfoot Courtois.

Within five minutes Chelsea were back in front, Burnley again exposed on its left flank.

Emerson Palmieri - making his first Premier League start - saw his deep cross come through to Moses, who rifled in past an unsighted Pope to restore the Blues' lead.

Dyche sent on Sam Vokes and the substitute striker headed a left-wing Gudmundsson corner straight at Courtois seconds after his 72nd-minute introduction.

A bright Hazard cameo from the bench helped Chelsea close out consecutive Premier League away wins after Sunday's comeback at Southampton, which it faces again at Wembley in three days' time.