Blues boss Antonio Conte paired Morata with Olivier Giroud in a rare front two for Chelsea and the duo made life hard for Sean Dyche's side, whose five-game winning streak came to an end. Online in-match use limited to 75 images, no video emulation.
Eight points separated Chelsea from Tottenham, and more importantly the final Champions League spot, when they kicked off, so it wasn't a shock to see Conte make six changes to his side, with an eye on Sunday's FA Cup semi final with Southampton.
Chelsea came into the clash on the back of a come-from-behind victory over Southampton, who they will face in the FA Cup this Sunday. Moses and Pedro were crucial to Chelsea's dominance and, had Àlvaro Morata not been ruled offside on countless occasions, then Chelsea could've gained some breathing space.
Four of Sean Dyche's squad - Tom Heaton, Nick Pope, James Tarkowski and Jack Cork - have been involved with England this season, but Pope and Tarkowski are the two most likely to make it on the plane to Russian Federation.
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But Conte believes the Spaniard showed he and Giroud can work more often as a partnership.
Conte added: "It won't be easy and we have to get three points every game".
The result ended Burnley's run of five successive wins and prevented them leapfrogging Arsenal into sixth, but there was no disappointment from Dyche. "We're closer than where we have been in the past where we have been with these sides".
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And coming on in the second half, they were just as dominant in the early going.
Olivier Giroud failed to connect a scorpion kick from a cross, but the ball ran through to Moses and the 27-year old squeezed his shot in at the near post for what proved to be the match victor.
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