It was the first time the Tigers had conceded a Premier League goal in five hours and 12 minutes but despite their sensational recent form the home team had looked nervous before conceding and were even more so afterwards.
Phil Brown's team surrendered possession far too easily, while two awful kicks up field from Myhill did little to help them settle.
And by the break Chelsea really ought to have extended their advantage.
A goalmouth scramble was eventually cleared by a Hull defender, while Malouda twice shot wide and missed a header from a Lampard cross that was slightly behind him. Myhill saved a Joe Cole snap-shot and, later, brilliantly tipped over a blistering strike from Anelka.
Yet despite Chelsea's superiority, Hull did have their moments and came perilously close to an equaliser when Cousin dribbled across the face of the opposition box before drilling the brilliant low strike that rebounded off the foot of the post.
Geovanni, displaying self-belief of staggering proportions, forced a save from Petr Cech with a free-kick that must have been 40 yards from goal while Marlon King headed straight at the Chelsea keeper from eight yards.
Brown sees positives in Chelsea loss
However, any hopes the home team harboured of forcing their way back into the contest ended minutes into the restart after a moment of defensive madness.
Kamil Zayatte, Michael Turner and keeper Myhill all stood and waited for someone else to deal with a long ball forward, that was allowed to bounce and then intercepted by the alert Anelka, who slotted home from a tight angle.
The off-colour Malouda smashed another good opening over the Hull goal and dragged another shot wide.
Chelsea continued to possess the greater threat without ever really giving the impression of over extending themselves.
Anelka should have doubled his tally but opted for placement instead of power and was denied by Myhill but Malouda finally found the net, slotting home from six yards after a superb low cross with the outside of his boot by Carvalho.
Hull, who play Manchester United at Old Trafford on Saturday, continued to press forward whenever possible and almost crafted an equaliser but substitute Richard Garcia headed wide of Cech's goal.
Hull City boss Phil Brown:
"To go behind after three minutes gave us an uphill task.
"We said at half-time that we had an extra day's rest after the weekend but we conceded a poor goal straight away.
"But we have 20 points from 10 games and we have to make sure that we continue to build on that."
Chelsea boss Luiz Felipe Scolari:
"I think Frank Lampard's goal was one of the best in the Premier League.
"It was a fantastic goal - only Frank Lampard can make this goal. It was one of the best goals I have seen in my life.
"He is a very intelligent player and he is a man that is never tired.
"There are many very good players in England, and one of the best is Frank."
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