But Rovers, who wasted a great chance to go ahead through Jason Roberts just before Ivanovic scored, were on top before the break and the defeat was harsh - despite an improved second-half performance by Ancelotti's men.
"Blackburn put us under some pressure and we were not able to play our football," the Italian said.
"We knew it would be difficult to win here because Blackburn are a very good team with a lot of strength and physical ability.
"So it is very important to win here to maintain our position at the top. We are in good condition now and I hope we improve on this victory.
"We were heading for a draw then we had the fantastic play of Zhirkov and we were able to win this game."
Blackburn boss Sam Allardyce felt his side could have done no more and deserved at least a point.
Allardyce determined to improve results
"They've got a punishing side to their game and they're ruthless. When they're being outplayed - and we outplayed them at times - they hang in there," Allardyce said.
"They're not in the game and they're not looking like scoring and we're in the ascendancy, then with three passes it's a goal. That outstanding quality can punish you at any time.
"It's one of those days where you play as well as you possibly can. It's pleasing to create chances against such a big team but it's the ultimate kick in the teeth when you don't take them.
"It's tremendously disappointing for the performance we gave to get the result we got. The performances are good but the points we are getting are just not good enough."
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