Morata scored inside two minutes after a fabulous pass by stand-in captain Cesar Azpilicueta and Pedro made it 2-0 by the interval with a powerful shot into the far corner.
Fellow Spaniard Pedro also found the net as Antonio Conte's side eased through their gears to thrash sorry Stoke.
"Morata played a good game".
Romelu Lukaku scored his eighth goal in as many games for Manchester United to seal a 1-0 victory away to Southampton on Saturday. Defender Azpilicueta has four assists for his six goals. Costa is likely to be watching his replacement from the stands at the Wanda Metropolitano.
In the second half, it was the Eden Hazard show - with the Belgian integral to the Blues' fourth goal.
Substitute Stoke striker Peter Crouch was somewhat fortunate to stay on the pitch when he went high on Fabregas with only a few minutes remaining, but referee Mike Dean only gave the Englishman a yellow.
With Chelsea facing the prospect of three games in seven days, Conte knows he will have to rotate his squad and believes he is now able to call on Hazard from the start, rather than manage him carefully from the bench.
He said: 'For sure it will be a really tough game.
Still, Alonso nearly fell afoul of Dean seconds before being replaced, with the defender foolishly taking a throw-in when the referee had already signalled it as a Stoke ball.
Conte then brought on Cahill for Marcos Alonso after the wing-back got away with a challenge on Diouf shortly after being booked for a foul on Allen.
"I am a Chelsea player, I signed a contract there and I love the club, but for now, I am a Stoke City player and my loyalties lie here", he said.
"This season Stoke have won at home against Arsenal and drawn against Manchester United".
There was a youthful feel about the Chelsea team.
MF Tiemoue Bakayoko, 7 - Set the pace early in midfield and initiated the move which resulted in Morata's opener but was culpable perhaps of having too many touches on the ball instead of passing quickly.