The result was never in doubt as the FA Cup holders completely outplayed their struggling Premiership opponents as they eased into the semi-finals.
First-half goals from Roy Keane, within 90 seconds of the kick-off, and Cristiano Ronaldo on the stroke of half-time, set the rhythm for the match before Scholes' double.
The visitors fielded a full-strength side as Sir Alex Ferguson made his intentions clear that the FA Cup was a competition he wanted to win.
In contrast Southampton boss Harry Redknapp rested his son Jamie and kept faith with goalkeeper Paul Smith instead of the fit-again Antti Niemi.
Despite conceding four goals, Smith again showed great promise and the defeat would have been even heavier but for some superb one-handed saves by the former Brentford keeper.
Smith could do nothing about United's first goal which was scored before most fans had sat down in their seats.
Just 86 seconds had been played when Quinton Fortune's corner was only half-cleared to captain Keane who cut inside before firing an unstoppable shot past Smith with the help of a deflection off Peter Crouch's head.
Southampton blew a golden chance to equalise in the ninth minute when Dan Higginbotham's long ball was flicked on by Crouch into the path of Anders Svensson who saw his angled drive saved by the knees of keeper Tim Howard.
United began to show their superiority soon after and were inches away from adding a second in the 23rd minute when Scholes dispossessed Olivier Bernard.
The former England midfielder played in Wayne Rooney whose shot was tipped onto the bar by Smith before the England striker somehow headed the rebound wide.
Smith was again called into the action in the 37th minute when he tipped Fortune's deflected effort over the bar before producing a wonder save from Rooney as he tipped his effort on to the post.
But United were not to be denied and they extended their advantage seconds before the interval.
Rooney's strong run down the left set up Ruud van Nistelrooy who teed up Ronaldo to blast in a second.
United were quickly out of the blocks at the start of the second half as well and added a third goal in the 48th minute through Scholes.
Van Nistelrooy was denied by the feet of Smith before the ball fell kindly to Scholes to hit home the third goal from 12 yards out.
Fit-again van Nistelrooy showed a hint of his former self in the 57th minute when his half-volley from an acute angle had to be tipped over the bar by Smith.
Ferguson made three substitutions in ten minutes midway through the second half but this did not give Southampton any more joy.
Their only notable effort of the second half came when on-loan striker Henri Camara flashed a dipping volley well wide of the mark.
United threatened to run riot and were in no mood to let up as they went in search of the fourth.
Fortune crossed for Rooney to head straight at Smith before they finally added another three minutes from time.
Rooney's pin-point ball sent van Nistelrooy clear down the right and his teasing inch-perfect cross found Scholes at the back post who duly obliged with a diving header from two yards out.
United could have added a fifth in stoppage time after good work by right-back Wes Brown.
The England defender swung in a cross from the right, substitute Alan Smith out-jumped Saints defender Calum Davenport only for his header to go inches over the bar.
MAN OF THE MATCH: Roy Keane (Manchester United) – Banished the disappointment of another Champions League exit by opening the scoring within two minutes. Kept United ticking over for the rest of the match when it would have been easy to take it easy against lack-lustre opponents.