Antonio Conte's champions have struggled in front of goal since the turn of the year but there were no such problems here during a comfortable 4-0 victory.
"We could have gone out with a different mentality in the second half".
Morata came on as a substitute in the 81st minute and his night was over in the 120th minute after he was also cautioned for diving before immediately being shown a second yellow for dissent towards the referee.
Eden Hazard opened the scoring for the visitors with a neat finish from inside the box and midfielder Willian added a second from 18 yards, after a slick move that he started, to leave Chris Hughton's side facing an uphill task. The frontman cut inside but was denied by a decent stop from Ryan. Chelsea have started games slowly this season, with a tendency to grow into the match but today was a contradiction of the past few months, as the Blues raced into a two-goal lead within just six minutes.
The Australia worldwide also denied Batshuayi before Caballero displayed astonishing reactions to keep out Tomer Hemed's 30th-minute header at the other end.
Referee Moss once again waved away Albion appeals for a penalty after a coming together with Bakayoko in the area, before booking Schelotto for his protests afterwards.
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The home side had a chance of pulling one back in the 50th minute, as Propper's header hit the post. Marcos Alonso was beaten to the ball by the determined Italian, whose poked effort was straight at the onrushing Caballero.
Hazard was not done for the day, putting the game beyond doubt in the 77th minute, coolly finishing past Ryan for league goal 101.
Schelotto's menacing press nearly grabbed a goal for the home side, but Caballero managed to get a hand on it.
There was still time for a fourth and wing-back Moses was the man to get it two minutes from time.
Chelsea climbed to third in the table as they moved level on points with second-placed Manchester United, who play away to Burnley later on Saturday. Subs: Krul, Huenemeier, Kayal, Murray (Hemed, 68), Baldock (Gross, 68), Izequierdo (March, 83).
Subs: Eduardo, Zappacosta, Sterling, David Luiz, Ampadu, Barkley, Musonda.