And though Hull did come back into the game, Chelsea always seemed to be biding their time.
Wright-Phillips, who was a constant threat in the first-half, drove in the cross and 18-year-old Sinclair curled home the first goal of Grant's reign.
Hull's hopes of a comeback were all but extinguished when Chelsea doubled their lead three minutes into the second half.
Not for the first time, Pizarro baffled the hosts' defence with his movement and his cross from the left was headed in by a combination of Kalou and Hull defender Damien Delaney.
When Sidwell's 25-yard drive made it 3-0 after only 52 minutes, a rout seemed to be on the cards but Hull held out and even went close to a consolation when Jay-Jay Okocha's free-kick fizzed narrowly over the bar.
Chelsea's only worry of the night came when Wright-Phillips limped off with an apparent hamstring injury - yet another concern for England boss Steve McClaren.
But his replacement Joe Cole did set up the fourth goal, providing the precise pass for Kalou to power home.
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