But without three defenders including Kurt Zouma, Stoke struggled to stifle Chelsea's counter-attacks and conceded again after half-an-hour when Darren Fletcher mistakenly chested the ball into the path of Pedro, whose right-foot shot gave keeper Jack Butland no chance.
Stoke stayed in the game until Morata finished them off with goals in the 77th and 82nd minutes, first dinking the ball over Butland and then tapping in to take his season's tally to six. Chelsea keeper Thibaut Courtois suffered an injury after falling heavily but played on.
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(Reporting by Neil Robinson; Editing by Toby Davis)
