A first-half goal from Scott Sinclair and three second-half goals, including an own goal from Damien Delaney, saw Avram Grant pick up his first win as Chelsea manager.
Hull created a chance minutes into the game as Stephen McPhee raced in on goal, but Juliano Belletti did well to tackle the Tigers frontman inside the box before he could fire off a shot.
Chelsea opened the scoring on 37 minutes as Shaun Wright-Phillips raced down the right and played a neat ball into the feet of Sinclair, who placed the ball with precision into the bottom right-hand corner of the net from just inside the box.
The home side came close to levelling the scores on 43 minutes as Jay-Jay Okocha swung in a low cross from the right and McPhee managed to get a shot away from eight yards, but the ball whistled just past Carlo Cudicini's left-hand post.
It was 2-0 to Chelsea three minutes into the second half as Claudio Pizarro played a ball into the Hull box from the left on to the head of Salomon Kalou who was challenged in the air by Delaney, with the Hull man forcing the ball into the back of his own net despite his best efforts to clear.
It was soon 3-0 to the visitors as Kalou found Steve Sidwell on the edge of the box and the ex-Reading man neatly curled the ball into the back of the net past the outstretched Boaz Myhill.
Okocha came close for Hull on 72 minutes with a free-kick on the edge of the box, as the Nigerian's curling effort floated just over the bar.
The Blues final goal came on 81 minutes via the ever-present Kalou, as Joe Cole played the ball into the striker, who calmly placed the ball into the back of the net from 18 yards.