Rooney followed up his hat trick in the Premier League this weekend by meeting Ryan Giggs' pass in the area and calmly slotting the ball into the net via the far post in the 24th minute of the first leg of their quarterfinal.
That was all United needed against an ineffective Chelsea, which had a late penalty appeal turned down but whose strikers Fernando Torres and Didier Drogba again failed to form the kind of potent partnership the club had hoped for.
"Keeping a clean sheet was important, but counterattacking was part of the game plan," United manager Alex Ferguson said. "Rooney is in great form, obviously, and he has given us a great chance of reaching the semi."
Ramires thought he had earned a penalty when he was brought down by Patrice Evra in the area in the 90th minute, but referee Alberto Undiano Mallenco waved play on despite TV replays showing clear contact.
Torres was then booked for diving when he fell in the area a minute later.
"It was a penalty and he needed to whistle," Chelsea manager Carlo Ancelotti said about the tackle on Ramires. "It was clear to everyone. But I understand it's not easy to give a penalty in the last minute of the game."
Ferguson, unsurprisingly, was of a different opinion.
"From where I was standing it looked a 50-50 (situation)," Ferguson said. "If it was (a penalty), it's the first decision we've got in seven years. I won't feel guilty about that."
With United sitting back to protect its lead, Torres came close to scoring in the 74th when his header forced a one-handed diving save from Edwin van der Sar, who also stopped Branislav Ivanovic's low shot from outside the area in the 85th as Chelsea pressed forward for the equaliser.
The hosts had looked sure to level in the 45th when Drogba broke in from the left and sent a loss cross into the area toward Torres, but the ball went past both the Spain striker and Van der Sar before bouncing off the far post. The rebound went straight back out to Frank Lampard, whose mishit shot was cleared off the line by Evra.
It was the closest the hosts would come to a goal and United now enters the return leg at Old Trafford on Tuesday with a big advantage. United has never been eliminated in the Champions League knockout stage after winning the first leg.
"We know it will be difficult to win there, but we have confidence we'll be able to do this," Ancelotti said. "We can do what Manchester did tonight. One chance and one goal. We don't need to trade a lot of chances."
After a tentative start from both teams, Michael Carrick started the flowing attack that led to United's breakthrough. Carrick sent a long ball down the left flank for Giggs, who broke into the area and squared the ball back toward Rooney, who slotted in his fourth goal in two games.
It was United's first effort on target.
"We lost the game and we have left ourselves a mountain to climb but we have to do it," Chelsea goalkeeper Petr Cech said. "I think we created chances and that was the key. They had their first chance and scored and we had some but we didn't score, and that's the difference."
Rooney is facing a two-game domestic ban after a profanity-laced tirade directed at a TV camera following his hat trick at West Ham on Saturday. But the England striker showed that he is returning to form just in time to help United in its push for a treble.
Torres, however, still looks far from his best as he remained scoreless since his 50-million pound transfer from Liverpool in January.
After being dropped to the bench against Stoke at the weekend, Torres started alongside Drogba up top instead of Nicolas Anelka. While the Spain striker showed plenty of intent, he often struggled to control the ball and his touch usually deserted him when pressured by a defender.
Torres showed a flash of his ability in the 31st when he broke free of Rafael down the left flank and passed off to Yuri Zhirkov. The Russian then returned the ball to Torres in the area, who downed it on his chest before shanking his attempt at an overhead kick.
Drogba attempted a similar overhead kick in the 56th after controlling the ball with one touch, but his effort went wide of the right post.
United's only setback came when defender Rafael collided with Didier Drogba shortly after the restart and had to be carried off on a stretcher with a suspected left knee injury. Ferguson said the Brazilian will be examined further on Thursday.
In the other quarterfinal today, Barcelona thumped Shakhtar Donetsk 5-1.
