The two teams went into the match at Ibrox, which had been dubbed 'The Battle of Britain', having already played two of their group encounters.
Somewhat surprisingly it was Rangers who topped the standings, having collected four points from their clashes with Stuttgart and Panathinaikos. From the same fixtures, United had amassed three points, having lost to the Germans 2-1.
So, Alex McLeish's side went into this fixture a decade ago knowing that a victory would not only tighten their grip on the summit, but it could also have serious repercussions where United's qualification chances were concerned.
It failed to inspire a positive start from the home side, though, and within five minutes United had broken the deadlock for what would be the only goal of the game.
Ruud van Nistelrooy - so often a scorer during his United career - turned creator on this occasion as he picked out Phil Neville with time and space inside the Rangers penalty area. From there, United's utility player was able to slot a low effort beyond the reach of goalkeeper Stefan Klos.
© Getty Images
The deficit prompted a positive response from the hosts, who created opportunities for Paolo Vanoli and Peter Lovenkrands, while up the other end Mikael Silvestre saw a headed effort cleared off the line by Mikel Arteta on the stroke of half time.
Both sides created openings after the restart, with Craig Moore having the best for Rangers, only to see his header hacked clear at the last minute by goalscorer Neville to secure all three points for the visitors.
"It was a great game of football, the atmosphere was terrific, the pitch was great and Rangers gave it everything," said United manager Sir Alex Ferguson, who spent two seasons with Rangers as a player.
Meanwhile, his opposite number McLeish added: "I was pleased with the performance and effort, but not the result."
United went on to win the group, while this defeat had a lasting impact on Rangers, who failed to collect another point from their remaining three matches and consequently finished bottom.
RANGERS: Klos; Khizanishvili (Ross 86), Berg, Moore, Ball; Ricksen, Arteta, Vanoli (Nerlinger 67), Lovenkrands; Arveladze, Mols
MAN UNITED: Howard; G Neville, Ferdinand, Silvestre, O'Shea; P Neville (Butt 85), Keane, Scholes, Fortune (Djemba-Djemba 90); Van Nistelrooy, Giggs