United were simply too good for Wolves and sealed their passage into the next round by half-time after first- half goals from Richardson and Saha.
Richardson helped himself to a second after 52 minutes as United easily followed up their midweek success against Blackburn Rovers that saw them book a place in the final of the Carling Cup.
They were never in any danger of suffering an upset at the hands of Wolves, who simply never got going.
Richardson's fifth-minute strike was the beginning of the end for Glenn Hoddle's side who couldn't get to grips with their more illustrious opponents and must now focus on reviving their play-off push.
Even with former United skipper Paul Ince leading from the front they never looked capable of becoming the first side outside the top-flight since Bournemouth in 1984 to beat United in the FA Cup.
Red Devils boss Sir Alex Ferguson made a surprise tactical switch, with Wayne Rooney and Rio Ferdinand starting the game in the centre of midfield and new signing Nemanja Vidic making his first start in the centre of defence.
United certainly didn't look any less potent in attack with Rooney in a withdrawn role and quickly made the breakthrough.
Wolves left-back Lee Naylor allowed Saha to get away from him and the Frenchman whipped a cross into the penalty area.
Central defender Joleon Lescott should really have cleared the ball but he let it slide past him and into the path of Richardson, who drilled a low drive past stranded goalkeeper Stefan Postma.
Wolves' sluggish start would have seen them slide even further behind but for Postma, who denied Richardson with a smart save at his near post to prevent the England international grabbing his, and United's, second.
That let-off finally sparked Wolves into life and they were inches away from grabbing a shock equaliser only seconds later when Carl Cort headed a Darren Anderton cross just over the bar from 12 yards.
But it was a rare moment of relief for Wolves.
While United may not have created a hatful of chances they dominated in terms of possession and when they did break through, Wolves again needed the heroics of Postma to keep them in contention.
The Dutchman pulled off another stunning save to push away a 20-yard drive from Saha in the 37th minute.
Three minutes later he dived bravely at the feet of Gary Neville to deny the England full-back, but there was nothing he could do on the stroke half-time when United made the game safe through the clinical finishing of Saha.
Wolves were undone by a long clearance up field by Vidic that Saha raced on to before driving a shot past Postma.
That was the game over as a contest and United underlined their supremacy seven minutes into the second-half when Richardson scored the simplest of goals.
Ironically it came just moments after Wolves had forced Edwin Van der Sar into his first save of the game when the former Fulham goalkeeper had beaten away a drive from substitute Colin Cameron.
The visitors surged straight forward and Ji-Sung Park fed a pass into the path of van Nistelrooy whose deft chip to the far post was headed home by Richardson.
The Premiership side eased off after Richardson's second, but Wolves' dismal day was perfectly summed up by Cort in the 63rd minute when he failed to grab a consolation goal by missing the target from just six yards.
Fittingly, the final Wolves word was left to Postma who denied Rooney a deserved goal in the 88th minute when he dived at the feet of the England striker.