Premier League - Ancelotti fires title warning
In the lead up to the game against Birmingham Ancelotti had publicly conceded the title, but the victory, courtesy of a brace from Florent Malouda and a Salomon Kalou strike, has once again opened the door.
But the Italian admitted Chelsea, who leapfrogged Arsenal into second place with the win, would likely have to claim maximum points from their remaining games.
Ancelotti said: "To win the title we'll need less points than last season.
"We won it with 86 last season. Now, with 80 points, United can win the title. They need 10 points."
He added: "In football, I learned that everything can happen in the game right up to the final whistle.
"You can win the title in the last minute and you can lose the title in the last minute.
"If we thought that one month ago we'd have a little chance to come back to fight for the title, I think that everyone could have said we were crazy.
"Now we are happy tonight because we've reached second place. We await to see what happens in the next five games."
However, Ancelotti refused to look too far ahead, saying: "Our aim is to try and win every game. After that, we can see our results and our position in the table.
"Six points at this stage with five games to go will not be easy, but we don't have to think we can or can't do this."
With Drogba delivering an imperious performance and the goals coming from the other two forward players, his decision was vindicated.
Ancelotti said: "Drogba, Kalou, individually, there were a lot of good performances. A lot of midfielders played really well.
"He (Drogba) has a strong personality. He knew that, with malaria, he didn't play his best.
"I think that now he's fit and he's showing fantastic quality. In one season, problems like Didier had can happen. We couldn't do anything about this.
"Now we have to be happy to see him playing fantastic football, but forget the past."
Birmingham manager Alex McLeish was left to reflect on a result that did them no favours in their battle to extricate themselves from a relegation dogfight.
Conceding the first goal inside three minutes was far from the best start and having been unable to recover from that early blow, Birmingham dropped a place to 15th.
McLeish said: "Shocking start. We did the same thing here last season and gave ourselves a mountain to climb. But we hung in there and never gave up."
McLeish said: "It's not normally something I'd encourage.
"When a player has been successful in scoring the penalties, as Craig has done, he should keep it.
"I'm sure they'll have a wee chat about it over the next few days."