City put in a spirited performance but were undone by goals from Malouda and Drogba at Stamford Bridge.
The Potters were pushed back from the start and Ryan Shawcross gave away a 9th minute penalty when he brought down Florent Malouda inside the area. Frank Lampard stepped up but Thomas Sorensen was upto the task and saved his spot kick, and also managed to safely push the ball away from goal.
The hosts were soon back on the attack and Drogba's 25 yard free kick was pushed away by Sorensen as City defended gamely, hoping that Jones could create his own opportunities at the other end, but the resistance was broken on the half hour as Terry sprinted forward before feeding Malouda, who finished smartly past Sorensen to finally give the home side the advantage.
The Danish keeper was alert to stop the lead being doubled on the stroke of half time as he raced off his line to beat Anelka to a Essien through ball.
Both sides exchanged close encounters early in the second half as Huth flicked a Delap throw in across goal and narrowly wide whilst Drogba nodded his close range header straight at Sorensen.
The Potters came close to drawing level when Glenn Whelan's 68th minute 25-yard thunderbolt cannoned off the bar and bounced on the line before flying to safety.
Fuller came off the bench and caused problems, two mazy runs halted by last ditch tackles from Essien and Alex before the game was sealed when Drogba converted the hosts second penalty of the game, after Sorensen had brought down Anelka.