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.
United then became favourites ahead of the second leg on March 10 when Rooney netted with headers after superb crosses from Antonio Valencia and Fletcher.
NEWS: Fergie thanks stars for red-hot Rooney
WIN: Tickets for Manchester United vs AC Milan
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."
ANALYSIS: Old legs and young Mister taught harsh lesson by youngsters and a guru
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.
Beckham sent in a free-kick and United left back Patrice Evra made a hash of a clearance, sending the ball across the box where Ronaldinho was waiting to lash in a volley off Carrick.
The Brazilian is still not quite as sparkling as he was in his heyday at Barcelona but he produced several cute flicks and forced Edwin van der Sar into three neat saves.
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.
England striker Rooney, who worked tirelessly all night upfront alone, then sent a looping header into the top corner on 66 minutes after Valencia crossed with one of his first touches of the ball having replaced the lacklustre Nani.
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.
Beckham, who won the 1999 trophy with United, had a decent game in his first appearance against his former club and shot over with a trademark free-kick.
NEWS: Beckham enjoys United reunion
‘The pure simplicity of the way Slot has managed the squad is probably the biggest thing I could say about him. It’s not broken, so let’s get on with it’: Liverpool legend full of admiration for Jurgen Klopp's successor at Anfield
‘I trained at Spurs and thought they’d give me a chance. But I received a letter thanking me but saying they didn’t think I was good enough – I was gutted’: How Tottenham missed out on signing Wales legend John Toshack
