Chelsea were troubled by Palace's organisation and speed on the counter-attack for long spells before Morata and Pedro Rodriguez scored to put the game out of reach, but their eighth win of the Premier League season keeps them unbeaten and brings them back to within two points of Manchester City.
The opening goal did finally arrive shortly after the half-hour mark when Morata collected Pedro's pass with his back to goal before instinctively shooting on the turn to leave Wayne Hennessey no chance from close range.
Morata gave Chelsea the lead by finishing well after good work from Pedro, but Palace levelled when a one-two with James McArthur caught David Luiz out of position and Andros Townsend beat Kepa Arrizabalaga with a fine drive.
Having struggled for much of his time at Stamford Bridge, Morata has now scored five goals in his last six appearances for the Blues.
It wasn't until Sarri summoned Hazard and Mateo Kovacic from the bench in the 64th minute that Chelsea took control. The Blues will be looking to maintain their undefeated start to the season but will face a tough test against Crystal Palace who has seemingly turned a corner following their 2-2 draw against Arsenal last time out.
"Last year was hard for me for many things". More often than not he is double-marked, with any opposition team safe in the knowledge they do not have much else to worry about.
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Last week against Burnley, Chelsea proved they can manage without Eden Hazard, scoring four goals with four different goalscorers and will have to do so again for at least a half with the Belgian not fully fit.
"I haven't played too many minutes, whether it be in the Premier League and the Championship, and at 22 it's not seen as enough by some people". Chelsea go 3-1 up! He improved also from a tactical and technical point of view.
While unbeaten Chelsea stay two points behind leaders Manchester City, Palace remain three points above the relegation zone after a seventh defeat in 11 league games.
8 - Sarri's starting XI encountered problems in the first half but his management of Morata is clearly paying off, and his substitutes - it's always nice to be able to bring on the Premier League's best player this season, isn't it? - turned a hard game in exactly the way he wanted.
69- Goal! Game over!
Barkley also forced his way back in the England squad.