Rooney, facing an FA charge for swearing live on TV last Saturday which could see him banned for two domestic matches, steered in a sweetly-struck 24th minute goal off the post after a flowing United build-up.
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United dominated the match for long periods with Rooney providing much of their inspiration in midfield and attack to leave Chelsea a huge task of saving the tie in the second leg at Old Trafford next Tuesday.
"Wayne was in tremendous form," United boss Alex Ferguson said in a televised interview. "He's given us a really great opportunity to get to the semi-final.
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"(He was) excellent, absolutely superb. (His) work rate, desire to play is marvellous. He got a lot of abuse tonight, he got a lot of late tackles on him but he got up and played. It shows the courage of the player. He takes great credit."
United defender Rio Ferdinand added: "He's a top quality player. Today, he showed touches of brilliance, some great touches, awareness and a great finish. He was buzzing around all over the pitch today and it was good to see."
With their Premier League title probably heading to Old Trafford and the European Cup their only realistic chance of a trophy this season, Chelsea were flat for long periods, and came closest to a goal when Frank Lampard saw his shot cleared off the line just before halftime by Patrice Evra.
They also had a strong claim for a late penalty denied.
United, who had not won at Stamford Bridge for 10 matches since 2002 but beat Chelsea to win the Champions League in the 2008 final on penalties, dominated with Rooney at the heart of much of their invention with some crisp passes and link-up play.
LAID SIEGE
With Rio Ferdinand reinforcing United's defence after 11 matches out with a calf injury, United looked composed at the back and inspired down the wings in attack and at one point laid siege to Chelsea's goal with the home defence just about managing to keep United at bay.
Although United deserved to go in ahead at the break, Chelsea almost equalised just before the interval.
Drogba played in a ball from the left to Fernando Torres, who, failing to get the touch that could have brought him his first goal for the club, saw the ball bounce back off Edwin Van der Sar's far post to Lampard.
The England midfielder, playing his 500th match for Chelsea, followed up the rebound only to see his effort cleared off the line by Evra.
The goal came after Michael Carrick found Ryan Giggs wide on the left before the 37-year-old found Rooney with his pass which the combative striker neatly steered home of the post.
Chelsea looked more dangerous as the second half progressed, and put United under more pressure in the closing stages.
Their pressure appeared to have paid off in stoppage time when they had a strong appeal for a penalty turned down by Spanish referee Alberto Undiano Mallenco after Evra appeared to bring down Ramires.
"Maybe it should have been a penalty but... it was about the time we got the benefit (of the doubt) here," said Rio Ferdinand.
Moments later Torres's miserable night ended with a booking when his name went into the referee's book for diving in the box.
