But Sir Alex Ferguson's side were more than aided by the benevolence of referee Mike Riley who sent off Southampton's Matt Paterson for violent conduct in the first half and then incorrectly awarded United a second-half penalty.
Goals from Danny Welbeck, Nani and substitute Darron Gibson earned United a simple passage into the next round.
United, who could afford to be without Cristiano Ronaldo and Carlos Tevez, were on top from the kick-off.
Their first opening arrived in the fifth minute courtesy of a fine through ball from Dimitar Berbatov.
The Bulgarian striker cleverly sent Ryan Giggs racing into the penalty area but the United winger's effort was far too high to trouble Kelvin Davis in the Southampton goal.
The gulf in class was beginning to show as the game settled with Anderson and Berbatov providing some moments of real quality.
In the 16th minute, Nani forced Davis into a fine save when the Southampton goalkeeper had to dive low to his right to deny the United striker.
Davis again kept Southampton on level terms two minutes later when he tipped a shot from Anderson over the crossbar.
But the goal United had been threatening finally arrived in the 19th minute through Welbeck.
Nani's corner was headed against the crossbar by John O'Shea and Welbeck had the simple task of nodding home the rebound from point blank range.
Moments later a brilliant ball from O'Shea almost put Berbatov through for a second goal but his shot was deflected wide.
United should have been two goals to the good in the 26th minute when Berbatov and Michael Carrick carved open the Saints back four.
Carrick ran on to lift the ball over the advancing Davis but with the goal at his mercy, Southampton defender Chris Perry produced a fine tackle to deny him.
However, Southampton's plight worsened in the 35th minute when Paterson was sent off.
The Southampton player, who had already been warned about a number of heavy challenges, was dismissed for violent conduct after a lunge on United defender Nemanja Vidic.
Moments later Rudi Skacel was booked for a foul on Nani and Riley felt the full fury of the disenchanted home fans.
The yellow card count increased in the 40th minute when O'Shea was booked after a foul on Davis.
Welbeck almost snatched a second at the near post in first-half stoppage time but Davis once again reacted well to tip the ball around the post.
Southampton's cause was well and truly lost a minute after the restart though when Riley awarded United a penalty for handball against David McGoldrick.
Oliver Lancashire brought down Welbeck on the edge of the penalty area and when Nani tried to get the ball over the defensive wall, Riley adjudged that McGoldrick had blocked its path with his arm.
The decision clearly a poor one as TV replays showed the ball hitting McGoldrick's head as he turned away.
Nani took full advantage though when he converted the spot-kick - sending Davis the wrong way.
Davis then denied Welbeck a second goal when he tipped his shot over the crossbar in the 49th minute.
United's dominance was such that they replaced Giggs and Carrick with Gibson and Rodrigo Possebon in the 55th minute.
Moments later Southampton's Andrew Surman let fly from 30 yards but his shot was straight at United keeper Edwin Van der Sar.
In the 62nd minute Welbeck made way for Wayne Rooney as United looked to set the seal a comfortable afternoon with a third goal.
Six minutes later Rooney was almost put through by a clever reverse pass from Berbatov but Davis spotted the danger and collected the ball off the United striker's feet.
United played the ball around with consummate ease as the clock ran down.
They were rewarded with a third goal in the 81st minute when Gibson smashed home a cross from Rooney.
Rooney almost had the last word but his 25-yard volley was well saved by Davis