The Spanish striker’s 31st minute opener handed the Blues the half-time advantage, but Roy Hodgson’s team brought themselves level again not long into the second 45 when Andros Townsend netted after a well-worked move.
However, parity would last just 12 minutes as Morata completed his brace, and soon after Pedro added a third to seal the win and continue the hosts’ unbeaten start to the Premier League campaign.
There was little goalmouth action until the 19th minute as Palace began well and nullified all Chelsea’s threats, and they even carved out a good opportunity of their own on a swift counter-attack that saw James McArthur pick out Wilfried Zaha who cut the ball back to the D where Max Meyer was lurking, however the German bent the ball over the crossbar.
But the bright start ended just after the half-hour mark when the hosts got themselves in front. Cesar Azpilicueta slipped a pass into Pedro’s path who had two bites of the cherry to pick out Morata, and when the ball did arrive at his feet the in-form striker swivelled to shoot low and beat Wayne Hennessey from close range.
It possibly should have been 2-0 three minutes later when Pedro saw a blocked shot spin towards Willian who smashed the ball into the net but was denied by the linesman’s flag, with replays suggesting he was level with the Eagles defence, but the Blues continued to probe and Morata went close to adding to his tally when a free-kick was nodded into his path by Marcos Alonso but he couldn’t keep his header down.
The half-time whistle came at a good time for Hodgson’s team as Chelsea were beginning to move through the gears, and after 15 minutes to compose themselves at the break, Palace came out positively for the second half and were rewarded on 51 minutes.
James Tomkins played an incisive ball into Townsend who laid it off to McArthur, and then raced forward. The run was spotted by the Scotsman who put the ball into space for Townsend to chase, and after leaving David Luiz in his wake he produced an accurate, composed finish into the bottom corner to level things up.
There was a slight chance for Palace to take the lead soon after when Meyer shot straight at Kepa Arrizabalaga from a very tight angle, but just after the hour mark the Eagles were indebted to Hennessey after he made a flying save to prevent Luiz’s header from a free-kick nestling into the top corner.
However, he would be beaten on 65 minutes when the hosts regained the lead. Moments after entering the fray as a substitute, Eden Hazard sent another free-kick into the box and it was allowed to travel right through to the back post where Morata was left unmarked, and he fired into the net to score his fifth goal in his last five Chelsea outings.
And then the game slipped out of Palace’s reach when Maurizio Sarri’s team added a third with 20 minutes to play. Hazard found Alonso who edged up the left touchline and was allowed to send a low centre towards the penalty spot, and Pedro was on hand to lash the chance past Hennessey and pretty much ensure the points would go to the west Londoners.
There were few opportunities for either side after that, and the only opportunities the Eagles had to reduce the deficit came when Patrick van Aanholt blasted well over against his former club, and in stoppage-time Townsend saw a shot deflect wide.
Morata should have completed his hat-trick when Chelsea broke from the resulting corner and Hazard unselfishly teed up the Spaniard who audaciously tried to flick the ball over Hennessey, but the Palace shot-stopper wasn’t to be caught out and prevented the scoreline flattering the hosts more than it already did.
Chelsea: Arrizabalaga, Azpilicueta, Rudiger, Luis, Alonso, Kante, Jorginho (Fabregas 80), Barkley (Kovacic 64), Pedro, Morata, Willian (Hazard 64). Subs: Caballero, Zappacosta, Cahill, Loftus-Cheek.
Palace: Hennessey, Wan-Bissaka, Sakho, Tomkins, Van Aanholt, McArthur (Schlupp 80), Kouyaté, Milivojevic, Meyer (Ayew 71), Townsend, Zaha. Subs: Guaita, Kelly, Riedewald, Puncheon, Sørloth.