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.
The improving Morata, though, scored his fourth goal in as many Premier League appearances, converting a free-kick from substitute Eden Hazard to set the Blues up a fourth consecutive win in all competitions.
And when Pedro turned in a cross from another Spaniard, flying left-back Marcos Alonso, Chelsea were able to celebrate moving up to second place in the table.
Chelsea struggled to break Palace down for much of a frustrating opening half, but they nudged ahead with their first shot on target in the 32nd minute.
Pedro's initial cross was blocked but he seized on the loose ball to fire in a low centre that Morata controlled well before drilling an excellent volley past Wayne Hennessey.
Chelsea quickly had the ball in the net again only for an offside flag to curtail Willian's celebrations.
But Palace levelled in the 53rd minute, McArthur sending Townsend clear of David Luiz to rifle a superb strike across Kepa and into the bottom-left corner.
Hennessey made an excellent save to keep out a David Luiz header but the goalkeeper was beaten in the 65th minute, Hazard making a rapid impact from the bench.
The Belgium star's wicked free-kick from wide on the right deceived the Palace defence and Morata thump in a low drive from the back post.
The points were secured for Maurizio Sarri's side when Alonso delivered the perfect cross for Pedro to slam home, but Morata wasted a great chance to seal his hat-trick in stoppage time with a failed chip claimed by Hennessey.
What does it mean? Blues keep pace with City
Manchester City sent a warning sign to their title rivals with a 6-1 demolition of Southampton earlier in the day, but Chelsea are right on their tails just two points back. Morata is finding form again and with Hazard fit after a spell on the sidelines with a back injury they are serious contenders.
Morata emerges as leading light
With Olivier Giroud watching from the stands due to a muscular issue and Hazard only fit enough for the bench, Morata was under pressure to deliver. The striker lost confidence badly last season but is getting back to his best, with a pair of fine finishes taking him to six goals in all competitions.
Frustrated Zaha on the fringes
Roy Hodgson paired Townsend with Wilfried Zaha in attack but despite the duo offering plenty of pace on the break they were starved of opportunities to show their speed. Zaha is Palace's key man but he did not attempt a single shot in a strangely muted performance.
Key Opta Facts
3 - Eden Hazard is only the third player to assist a goal in three consecutive substitute appearances in the Premier League, after Tomasz Radzinski for Everton in March 2004, and Arjen Robben for Chelsea in April 2005. Magic. pic.twitter.com/XXRsafmD0K— OptaJoe (@OptaJoe) November 4, 2018
- Chelsea are undefeated in their opening 11 Premier League matches of this season (W8 D3 L0) - they won the league in the previous two seasons they achieved this (2005-06 and 2014-15).
- Morata has scored four goals in his last four Premier League games – one more than in his previous 23 appearances in the competition combined (3).
- Townsend has scored three Premier League goals against Chelsea – more than he has against any other opponent.
- Sarri is unbeaten in his first 11 Premier League games as Chelsea boss – this is the joint-longest unbeaten start by a Premier League manager, equalling the record set by Frank Clark in 1994.
- Pedro has ended on the winning side in 39 of the 40 home top-flight matches he has scored in during his career (26 of 27 with Barcelona, 13 of 13 with Chelsea), drawing the other with Villarreal in January 2010.
Chelsea head to Belarus to face BATE in the Europa League on Thursday, while Sarri will hope Hazard is fit to start against Everton at Stamford Bridge three days later. There is another London derby next weekend for Palace, who are at home to Tottenham on Saturday.