After a penalty shout for handball against Stephen Kelly was turned down by referee Michael Oliver, the deadlock was broken three minutes before the interval. Ashley Young's dangerous cross went over Brede Hangeland's head and under Riise's studs. Evans pounced to show great awareness to tee up Rooney and the striker gleefully smashed home, immediately acknowledging the Northern Irishman's part in the goal.
Relaxed, the Reds started the second half in complete control but were unable to find another way past Schwarzer. Giggs' excellent pass released Valencia but the Australian keeper saved well, with Riise getting to the rebound first to stab it behind to safety.
Aaron Hughes survived a nervous moment when dealing unconvincingly with a Rafael centre before a trademark curler from Young brought the best out of Schwarzer, who dived to parry. Damien Duff made a vital block as Fulham continued to smother many of the United attacks and Sir Alex decided to shake things up in attack by replacing Welbeck with Javier Hernandez.
The champions kept knocking on the door but Giggs dragged a left-foot attempt well wide and Schwarzer made a superb double stop to keep out Young following a cross from Valencia. When the ball came out to Giggs, Hangeland made yet another vital intervention to keep the visitors within touching distance.
With Rio Ferdinand and matchwinner Rooney substituted as the clock ticked down, the capital club were able to ensure it was nervous finale as Old Trafford grew ever more tense. And there was an almighty scare when substitute Murphy went down under Michael Carrick's challenge towards the end of normal time but Oliver waved 'play on' instead of pointing to the spot. Fittingly, Evans capped an inspirational individual performance by heading away