Ancelotti paid tribute to his goalscorers as the Blues banished the nightmare of their Champions League final defeat in the Luzhniki Stadium two years ago.
The victory puts them three points clear at the top of Group F and a win over the Moscow side at Stamford Bridge in a fortnight will guarantee the Blues a first-place finish.
"I think that we played a good game," said Ancelotti. "It was not an easy game because Spartak, above all in the second half, played well.
"But we established good control in that first half, scoring two goals, and then controlled it defensively in the second. We played well at the back, above all Petr Cech, who made some fantastic saves.
"Anelka showed his qualities and ability to play in front. He's comfortable playing up there when there's no Didier Drogba. He's a fantastic player and can play in all the positions across that front line."