He immediately started to repay that fee by scoring in the Charity Shield against Liverpool and followed that up with a brace against Fulham on the opening day of the Premier League season.
Then, in the 33rd minute, Van Nistelrooy doubled his and United's tally when he pounced inside the area after Southampton had failed to clear an Ole Gunnar Solskjaer corner.
The Norwegian turned scorer five minutes before the break to effectively end the game as a contest, as he volleyed in a lofted pass from Nicky Butt.
Seven minutes after the restart, Van Nistelrooy completed his hat-trick, again converting a pass from Scholes that had split the away side's rearguard.
Just 60 seconds later Gordon Strachan's visitors reduced the arrears when Juan Sebastian Veron gifted the ball to Paul Telfer, who in turn picked out Marian Pahars. From there, the Latvian was able to score from close range.
Sir Alex Ferguson reacted to the goal by introducing David Beckham and Ryan Giggs into the action and the latter of the wing duo played in skipper Roy Keane in the 72nd minute to make it 5-1 to the home team.
The scoring was then completed 12 minutes from time when Southampton gifted full-back Phil Neville the time and space to drill in from 18 yards out.
MAN UNITED: Barthez; Phil Neville, Gary Neville, Blanc, Silvestre; Veron (Beckham), Keane (Wallwork), Butt, Scholes; Solskjaer (Giggs), Van Nistelrooy
SOUTHAMPTON: Jones; Dodd, Williams, Lundekvam, Bridge; Telfer, Davies (Ormerod), Svensson (Delap), Marsden; Pahars, Beattie