United surprisingly fell behind in their Group F tie against the Scottish champions when Jan Vennegoor of Hesselink took advantage of a Rio Ferdinand error before firing a low shot past Edwin van der Sar.
|Manchester United celebrate when they win 3 - 2 over Glasgow Celtic|
Two subsequent goals from Louis Saha left United leading 2-1 but a well-taken free kick from Shunsuke Nakamura two minutes from halftime sent the sides in level at the break.
However, United were back in front within 70 seconds of the restart as Ole Gunnar Solskaer, continuing his latest and most successful comeback from longterm injury, tapped the ball into an empty net after Saha's initial shot was blocked.
Also in Group F, FC Copenhagen and Benfica played out a scoreless draw.
In Group E, Olympique Lyon showed Real Madrid still have some way to go before they can be counted as serious challengers for this year's title, easily defeating the Spanish giants 2-0.
Brazilian Fred scored the opening goal for the French champions after 11 minutes, calmly lobbing the advancing Iker Casillas in the Real goal. Portuguese international Tiago deservedly doubled Lyon's lead on 31 minutes after being played free by Sydney Govou.
In the other match in Group E, Steaua Bucharest gave a further indication that Real won't have an easy passage out of the group, putting in an impressive performance to beat Dynamo Kiev 4-1 in the Ukraine.
Sorin Ghionea headed the Romanians in front after just three minutes and although Serhiy Rebrov equalized for Kiev, a header from Valentin Badea and two further goals from Nicolae Dica sealed an impressive win.
Six time champions AC Milan may have only earned the right to play in the Champions League through an Italian appeal court but the Serie A side showed they will be a force to reckon with as Carlo Ancelotti's side cruised to a 3-0 away win over AEK Athens in Group H.
Veteran Filippo Inzaghi got Milan's opener on 17 minutes, heading home 38-year-old Milan captain Paolo Maldini's cross, while a totally unmarked Yoann Gourcuff made it 2-0 four minutes before the break after Kaka found the Frenchman with a pin-point cross.
Kaka got on the scoresheet himself 14 minutes from time, stroking home a penalty after Inzaghi was fouled in the area.
In the other match in Group H, Anderlecht and Lille drew 1-1. Nicolas Pareja put the home side in front on 41 minutes but Nicolas Fauvergue equalized for Lille 10 minutes from time.
Last year's beaten finalists Arsenal got their Group G campaign off to a winning start, beating SV Hamburg 2-1 away.
Hamburg played most of the match with 10 men after goalkeeper Sascha Kirschstein saw red on 10 minutes for pulling down Robin van Persie in the area.
Gilberto stepped up to put the Gunners (Arsenal) in front from the subsequent penalty and Tomas Rosicky made the three points safe on 53 minutes with a superb strike from outside the area.
Boubacar Sanogo got a consolation goal for Hamburg in injury time to make it 2-1.
Also in Group G, Porto and CSKA Moscow played out a scoreless draw.