Nine-time winner Real Madrid, four-time champion Bayern Munich, two-time winner FC Porto, Lyon, Arsenal and Villarreal also advanced to the knockout phase with a game to spare.
That means 10 have already made it with Juventus, Barcelona and Sporting Lisbon also having advanced.
Cristiano Ronaldo had a shot pushed onto the crossbar by goalkeeper Diego Lopez but the draw meant that both United and Villareal have nine points at the top of Group E. Even though Aalborg came from behind to beat Celtic 2-1, it only has five points and the Scottish champion has two.
"I was satisfied with our second-half performance and I thought we were better," United manager Alex Ferguson said. "It takes us into the next stage and that's the name of the game."
Raul Gonzalez netted Real Madrid's seventh-minute goal in a 1-0 victory at BATE Borisov which meant it joined already-qualified Juventus from Group H. Juve was held 0-0 by Zenit St. Petersburg, last season's UEFA Cup winner which can't catch either of the powerhouse teams.
"We wanted to settle the issue of qualification here, tonight," said Madrid manager Bernd Schuster, who is under fire back home after some poor recent results. "We defended very well, and starting quite far from our penalty area."
Two goals by Miroslav Klose and one by Luca Toni helped Bayern Munich cruise into the knockout phase with a 3-0 victory over Steaua Bucharest although coach Juergen Klinsmann was anxious after a scoreless first half.
"After we missed many early chances I was worried that we would give away a stupid goal," Klinsmann said. "But we knew that eventually we would score. We are very pleased, it looked very good."
Lyon won 2-1 at Fiorentina which means both are out of reach with 11 points in Group F.
Jean Makoun and Karim Benzema put Lyon in control in Florence with goals in the first 27 minutes and Alberto Gilardino replied in the 45th.
Nicklas Bendtner's 87th-minute winner for Arsenal secured a 1-0 win over Dynamo Kiev in Cesc Fabregas' first game as captain, giving the Gunners 11 points as well.
"It is important to win the first game," said the 21-year-old Fabregas, who replaced William Gallas as captain following the Frenchman's revelations about bustups between Arsenal players.
"We did very well, and the attitude was spot on from the first minute to the last. It is a great result. We know for sure we are through to the next round so that is fantastic."
FC Porto also made it to the last 16 with a 2-1 victory at Fenerbahce with two first half goals by Lisandro Lopez.
Barcelona and Sporting Lisbon, currently first and second in Group C, play on Wednesday having already made it to the last 16.
