The much-maligned Alberto Gilardino struck a double in the amazing triumph, which came 24 hours after president Silvio Berlusconi had admitted Milan were in crisis.
"I'd say that we had a bit of a nervous start, but after taking the lead we built up this win. It was a delicate and difficult game, but certainly changes the atmosphere surrounding the club," said Ancelotti at the final whistle.
"Our second half was of a very high level, alternating possession with quick moves into space. The two strikers played brilliantly.
"The break for international duty comes at the right time, as it allows us to recover some players we had out injured. We accept criticism, but some went over the line. In any case, it has been a complicated week."