Fulham responded with a late goal from Aaron Hughes, but in truth the center half endured a horrendous evening having conceded the penalty and been at fault for the majority of the goals.
The last two times the Red Devils have seen off the Cottagers in the FA Cup, they have gone on to win the competition and Sir Alex Ferguson will be hoping that omen bears fruit again, as his side chases another treble.
United began in typically blistering fashion as it mustered up a chance immediately from the outset as Rooney engineered a chance, which was eventually deflected wide for a corner.
From the subsequent set-piece, the home side would be handed a spot-kick, quite literally.
Rooney's in-swinger hit the hand of Hughes as he jumped with Chris Smalling and Giggs, who was elected as the spot kick taker after Rooney's recent misses, dispatched aplomb despite the best efforts of Mark Schwarzer.
After the early setback, Fulham looked to get the ball down and resume its slick passing game but lacked Giorgios Karagounis' calm head in midfield, and the hosts looked to hit the Cottagers on the counter every time they seized on the loose ball.
Ferguson's side was incisive with its passing in the final third and an eye-of-the-needle through-ball from Rafael found the overlapping Nani, whose cutback to Rooney was ultimately fired onto the bar from Schwarzer's vital save.
You sensed the second goal would ultimately have a huge bearing on the end result, and the hosts sought to claim it as they were denied a second penalty before missing a series of presentable chances.
Giggs and Patrice Evra linked up well down the left-hand side and when the Welshman freed the latter, Damien Duff stuck out his arm to divert the ball out for a corner, but to the astonishment of the United players and Old Trafford crowd, Mark Clattenburg refused to award another penalty.
Rooney was then denied by Schwarzer once again, with the Australian veteran desperate to give his side a fighting chance in the second period, while Nani also went close on two occasions but after working himself some space, he fired wide each time.
It appeared United felt it had been on the receiving end of a grave injustice and set about putting the record straight as it started the second-half with new-found verve and vigour.
And after Berbatov wasted a fantastic chance for Martin Jol's side, the Cottagers were duly and emphatically punished by a quickfire double from Rooney and Hernandez.
Rooney, who was at the center of everything good about United's display, was slipped in by a wonderful Anderson slide rule pass and after controlling and checking back inside Hughes, the 27-year-old smashed a ferocious effort past the hapless Schwarzer.
The 40-year-old had stayed out on the pitch at half-time to practice his shot-stopping, but it seemed like a waste of time when United stretched further clear.
Jol and Schwarzer will quite rightly be asking questions of the defense, as they stood off Nani and Rooney, leaving the latter with the simplest task of locating Javier Hernandez in the six-yard box, and the predatory Mexican made no mistake.
Fulham looked visibly deflated and the game was effectively over as a contest but United was hungry for more to see off any lingering threat. Hernandez sealed the West Londoners' fate.
The space offered to Hernandez and Rooney was frightening as United attacked at will but although the visitors' defending was slack, to say the least, the Mexican's effort was fortuitously diverted past his own keeper by Hughes, who had a torrid night defensively.
The Northern Irishman proved no match for United's illustrious strikeforce at times but showed his fellow teammates how to do it in front of goal as he grabbed a consolation strike when he headed Karagounis' corner home at David De Gea's near post.
Fulham looked to grab another and almost did when substitute Hugo Rodallega arrowed a shot wide but another goal would have made for a misleading scoreline, with Ferguson's men safely navigating their way through to Sunday's draw for the fifth round.
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