'Super Pippo' came on as second half substitute to score two goals and set up Kaka with another, leading the European champions to a vital away win.
"He’s a consummate professional, Inzaghi worked hard in this period despite the fact I didn’t give him the chance to play," Ancelotti said after the game.
"I could see him champing at the bit, but also acting like a real professional even though he was suffering. He was brilliant both on the night and in preparing for it, as he was always ready."
The Italy striker, who scored two goals in last year's final to hand the Rossoneri the title in Athens, has been recently relegated to the bench in favor of Alberto Gilardino.
However, it is likely that both strikers will play second fiddle when the injured Ronaldo regains his fitness.
The Brazilian icon returned to the Milan squad for the first time in three months, but Ancelotti had his reasons to keep him on the bench.
"Considering the way the game was going, I decided to be prudent, as it wasn’t wise to introduce Ronaldo in this cold when he had not played in three months. He will have time to give his contribution," said the Milan tactician.
Unselfish link
Milan star Kaka hailed Inzaghi's 'altruistic' link with him after both players combined together brilliantly to round off the victory.
"He set up the second for me and I returned the favor in the third. We were both feeling rather altruistic tonight!" said the talented playmaker.
The competition's top marksman last year had a fine chance to top the scoring charts on Tuesday when he was one-on-one with the keeper, but he unselfishly provided Inzaghi with his second.