Rooney had come under fire -- and earned a two-match ban, along with front-page headlines -- for a foul-mouthed tirade at television cameras after scoring his hat-trick in a 4-2 win over West Ham last week.
After firing home decisively at Stamford Bridge yesterday, the England forward resisted any temptation to scream out his feelings as he raced towards the cameras behind the goal after sweeping home Ryan Gigg's low cross in the 24th minute.
Manager Sir Alex Ferguson and defender Rio Ferdinand saluted Rooney, the England defender telling ITV sport: "He's a top quality player - he showed flashes of brilliance."
For Ferguson, Rooney "was important on the counter-attack and he was in tremendous form and he has given us a great chance of reaching the semi."
He added: "It's still in the balance (but) it's good result for us. That away goal does mean something."
Tuesday's fireworks comprising Real Madrid's four-goal salvo against the other English survivors, Tottenham, and Schalke's 5-2 demolition of holders Inter Milan in the San Siro had set the entertainment bar sky-high.
Although the goal count in London was lower, the full-blooded nature of the encounter kept the fans on the edge of their seats as both sides set about their business with gusto.
United, who saw off Chelsea in a penalty shootout in the 2008 final, gambled on the fitness of England veteran Ferdinand following more than two months struggling with a calf injury and his experience was a boon in a tense affair.
Rooney's strike gave United their first win at Chelsea in nearly a decade and the three-time European champions are now clear favourites to advance to a likely semi-final against Schalke.
Chelsea came agonisingly close to levelling moments before the break when Didier Drogba crossed into the danger zone only for misfiring sidekick Fernando Torres to fail to get a touch, the ball bouncing on to clip Edwin Van der Sar's far post.