The Tigers had gone into the game at the KC Stadium trailing the Blues only on goal difference but a stunning strike from Frank Lampard after just two minutes established superiority.
Lampard found the net with a delicate left-footed chip from the edge of the box after Paul McShane had dispossessed Florent Malouda but failed to clear.
Hull tried to respond through star forward Geovanni but the Brazilian was denied a free-kick after running into Ricardo Carvalho just outside the area.
Lampard tried his luck again from a free-kick 30 yards out but could not find the target.
Hull were inches away from an equaliser after 22 minutes as former Rangers striker Daniel Cousin's low shot from 20 yards took a slight deflection and beat Cech, only to bounce back off the post.
Geovanni also tested Cech with a long-range free-kick, but the Chelsea keeper beat the ball away after it bounced awkwardly in front of him.
Hull were then forced to sit back for a spell and survived a scare as Malouda found room to shoot but fired over.
Nicolas Anelka went even closer with a ferocious drive just before the break but Myhill did brilliantly to tip over.
Cech was also in action again, keeping out another Geovanni free-kick and a King header.
Chelsea doubled their lead in the 50th minute as Anelka capitalised on uncertainty in the home defence.
Michael Turner and Kamil Zayatte switched off as they allowed a ball to bounce between them. Myhill came forward to gather but was caught in two minds as he reached the edge of the area and Anelka nipped past him to turn the ball home.
Malouda made up for some earlier misses as he reacted first to stab home a Carvalho cross and put the game beyond doubt after 75 minutes.