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.
Anelka showed his worth with both goals, both expertly finished, to take his tally to seven in his last six Champions League games.
Though Torres still laboured with a heavy touch he did show the green shoots of a partnership with the Frenchman.
Florent Malouda and Ramires, who seems to be improving with every match after taking an age to adapt to the English game, were the wide men and though they were hardly Gareth Bale or Theo Walcott, they did generally maintain their shape with Frank Lampard and Michel Essien in the middle.
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."
BIG SULK
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.
Chelsea, in fifth place will be 15 points off the pace if United win at Wigan Athletic on Saturday but, having finally found some rhythm and, seemingly, the best way to accommodate his 50-million pounds striker, Ancelotti will not want to lose momentum with a home defeat against his major domestic rivals.
If he maintains the 4-4-2 system, with Drogba again on the bench, he runs a double risk. The most obvious result could be a three-month sulk from his former main striker, not something he can afford as he continues the delicate task of bedding in Torres and keeping up morale.
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.
Ancelotti, of course, was loo
