The Danes looked to be still in winter hibernation, not having played a competitive match since December they failed to put Chelsea under any real pressure and can just about write off the last-16 tie.
Chelsea, out of the FA Cup and trailing leaders Manchester United by 12 points in the Premier League, needed a good result and, just as importantly, needed to find some cohesion.
They got both via Ancelotti's decision to revert to a 4-4-2 formation that accommodated Fernando Torres and Nicolas Anelka but left Didier Drogba out in the cold.
The big loser in the deal looks to be Drogba, and though Ancelotti said he needed a rest after playing 120 minutes against Everton on Saturday it looks increasingly likely that when it comes to Chelsea's attack, three is a crowd.
"Torres and Anelka were fresh and, together, they played well. Lampard also had good combination with Fernando," Ancelotti said.
"The movement we were able to do in front with Anelka and Torres, they started well the game and it was easier to attack.
"The players are accepting my decisions without problems, and this is important. There was no problem with Drogba, he was focused with the other players."
Drogba, 33 next month, did come on for Anelka for the last 20 minutes but the game was all but over by then and for all Ancelotti's talk of harmony, he is not the sort of player to sit happily on the bench every week.
Though the Champions League has become Chelsea's only realistic chance of a trophy this season, the key to the remaining three months could be next Tuesday's Premier League game against United at Stamford Bridge.
Secondly, United's powerful midfield and attacking width in the shape of Nani and Ryan Giggs could overwhelm Chelsea's middle rank and destroy the fragile confidence achieved from Tuesday's victory.
