كتب : Amro Hassan
A Dimitar Berbatov brace (30, 51) and a Wayne Rooney strike (76) kept United on course for qualifying past the competition's group stage.
Despite controlling the game from the very first minute, United were stunned by two Celtic attempts that might have changed the score line.
On the 11th minute Aidan McGeady cut inside the United box and fired a left-footed effort that was brilliantly saved by Edwin Van Der Saar.
Eight minutes later the visitors went close again, and this time through Gary Caldwell who saw his powerful volley tipped over by the Dutch keeper.
The home side restored their grip over the tie, and on 30 minutes Berbatov put them ahead after capitalizing on Cetic's poor defense to a Cristiano Ronaldo corner.
Darren Fletcher had the chance to double United's tally. The Scot was found unguarded on Celtic's far post but he blew his shot wide.
United dominated the game after the interval, and in the 51st minute Berbatov added his personal second from a rebound after Artur Boruc poorly parried Ronaldo's free kick.
Five minutes later, Boruc could have paid for another mistake but this time Rooney's rebound went over.
The England striker made up for his earlier miss fifteen minutes from time. United hit their visitors on the break and this time Rooney placed his shot into Boruc's bottom corner.
In the same group, Villareal thrashed Aalborg of Denmark 6-3 at the Madrigal.
Aalborg showed they were no pushovers when they took the lead on 20 minutes through Marek Saganovski.
Giuseppe Rossi equalized for Villareal eight minutes later before the hosts took the lead on 33 minutes thanks to a Joan Capdevilla strike.
Aalborg once again went on top courtesy of a Tomas Enevoldsen 36th minute strike.
In the second half substitute Joseba Llorente turned the game around for the Yellow Submarines by netting a hat trick.
His first two came in the space of three minutes (67, 70) before Andreas Johansson pulled one back for Aab.
Robert Pires put the result beyond doubt for Villareal by scoring in the 79th minute before Llorente scored his third five minutes later.
Villareal and Manchester United are joint leaders of the group with seven points while Celtic and Aalborg at the bottom with one point each.