Seven-times champions Milan, who had never lost to United at home or over two legs, were quickly ahead when Ronaldinho's volley deflected in off Michael Carrick following a free-kick from former United midfielder David Beckham.
The hosts had a series of other chances before Paul Scholes swung at a Darren Fletcher cross with his right foot, the ball hit his left shin and then bobbled in off the post.
Substitute Clarence Seedorf pulled one back five minutes from time with a superb backheel but Milan failed to equalise after huge late pressure where United's Carrick was dismissed for two bookings.
"We started slowly but overall I thought we were the better team, but I was frustrated in the first half because some people were not doing their jobs right," said Rooney.
"At 3-1 I thought we were the only team likely to score again. But to win 3-2 at the San Siro is still a great result."
United fans again noisily protested against owners the Glazer family in Milan's main square before kick-off but they were soon silenced at a rocking 80,000 capacity San Siro.
Last year's runners-up found their way back into the game, however, and scored their first European Cup goal against Milan in the San Siro thanks to Scholes' 36th minute mishit.
An unmarked Rooney then proved again why he is fast becoming one of the best players in the world when he guided in Fletcher's well-weighted cross as United went a record 16 away matches unbeaten in the Champions League.
