Youngsters Danny Wellbeck and Darron Gibson both scored their first FA Cup goals either side of a Nani penalty to lead United to a fourth round clash with Tottenham.
Sir Alex Ferguson could even afford to leave Cristiano Ronaldo back in Manchester and Wayne Rooney on the substitutes' bench as his side kept up their assault on a unique Premier League, Champions League, Carling Cup and FA Cup quadruple
United could have taken the lead inside the opening 15 minutes when home goalkeeper Kelvin Davis produced a fine save to turn away Ryan Giggs' powerful shot, after the veteran Welshman had played a neat one-two with Dimitar Berbatov.
Davis did even better to fingertip Anderson's 20th minute piledriver over the woodwork and deny the Brazilian his first-ever goal for United.
There was nothing Davis could do to stop Wellbeck giving the Premier League champions the lead from the resulting corner.
Wellbeck was quickest to react when John O'Shea's header from Giggs' centre rebounded off the crossbar and stooped to nod home from four yards.
Southampton's hopes of an upset were dashed eight minutes before half-time when Matt Paterson was shown a straight red card for a late challenge on Nemanja Vidic.
Referee Mike Riley was at the centre of more controversy three minutes after the interval, when he awarded United a penalty for David McGoldrick's handball from Nani's free kick.
Television replays suggested the ball had struck McGoldrick's shoulder, but Nani ignored Southampton's appeals to send Davis the wrong way and pick out the bottom left corner.
Ferguson's side created countless chances to extend their lead, before substitute Gibson had applied a close range finish to Rooney's 81st minute cross to make it 3-0.