Chelsea had taken a 20th-minute lead through a Kevin Long own goal and was well in control of the game.
'On the ball they confirmed nice hyperlink (play), an awesome mixture.
Chelsea are now without usual left-back Marcos Alonso, who is serving a three-game suspension, and Emerson has a chance to stake a claim for a first-team role while he is out.
However Conte was proud of Morata's efficiency after beginning him alongside Olivier Giroud for the primary time, and indicated he may do it once more in Sunday's FA Cup semi-final in opposition to Southampton.
"There is a gap between us and Tottenham - we are talking about five points and there are four games to go", he told reporters. "We deserved to win".
"Allegri, yes, I think he's the type of person that would get them players playing his way and be playing with the players he's got".
"But I have to see his whole performance and it wasn't possible in the past to play with two strikers".More news: Israel ministers defend soldiers appearing to rejoice in shooting Palestinian
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Chelsea have the opportunity to increase the pressure on their London rivals when they travel to Swansea on 28 April.
Burnley's resistance lasted 20 minutes but broke when Gary Cahill's long ball from defence found Moses on the charge.
However, Burnley's hopes of leapfrogging Arsenal into sixth were dealt a blow by a first defeat in seven games.
With Giroud and Morata adopting an impressive and early understanding, the former set up the latter for a shot from a wide angle which Pope did well to save via an outstretched boot after 10 minutes.
The starting line-up had raised eyebrows, notably the inclusions of Tiemoue Bakayoko and Emerson Palmieri, while misfiring Alvaro Morata also had another night to forget. "Giroud and Morata played a fantastic game and sacrificed themselves for the team".
The Stamford Bridge outfit claimed a 2-1 victory over Sean Dyche 's after manager Antonio Conte experimented a new formation which accommodates Giroud and Morata in the same lineup.
The hosts briefly threatened to fight their way back into the game on the half-hour, but a period of prolonged adventure yielded nothing more than a half-chance for Barnes.