Bayern Munich 2-1 Celtic
Roy Makaay started to pay back his £18m transfer fee with a double that brought Bayern Munich from behind to thwart a brave Celtic challenge in Munich.
But it was a blunder by goalkeeper Magnus Hedman that handed the Dutchman his winning goal four minutes from the final whistle and ended Bayern's run of six Champions League games without a win.
Alan Thompson looked to have given Celtic a dream start to their Group A campaign when he gave the Glasgow side a deserved lead midway through the second half.
But Makaay followed a superb volleyed equaliser with a cross that Hedman failed to gather and allowed to curl into the far corner of the net.
Celtic, who were without captain Paul Lambert in midfield, threatened first when Didier Agathe sprinted clear of Bixente Lizarazu.
His low cross was met by Chris Sutton at the front post, but the forward, returning to the side after injury, saw his effort deflected into the side netting.
Bayern recalled big guns Michael Ballack, Ze Roberto and Claudio Pizarro after they missed the weekend defeat to Wolfsburg through injury.
But it took them until the 26th minute to threaten, an Owen Hargreaves free kick bending dangerously past Magnus Hedman and the far post.
But Celtic still looked the more dangerous and a Bobo Balde header from an Alan Thompson free-kick forced Oliver Kahn to turn the ball over the bar.
Robert Kovac had to clear from in front of his own goal after a superb Larsson cross to the back post found the head of John Hartson.
Bayern striker Makaay had been starved of opportunities but almost pounced at a corner early in the second half, his header flying just over the bar.
The Dutch international then sent a cross to the back post that found Ze Roberto, who headed wide.
And just when Bayern looked to be taking control, Celtic took the lead after 57 minutes.
An Agathe cross to the back post evaded Hartson, but Thompson came diving in at the back post to head the ball in off the near post.
Alan Thompson had given Celtic a deserved lead
Bayern were stunned but almost equalised on the break when a low Ballack drive from 20 yards was saved superbly by Hedman.
Claudio Pizarro almost deflected a Thompson corner into his own net, but Bayern bounced back to equalise.
A poor defensive header from Stanislav Varga fell to Makaay 22 yards out and the striker's sweetly struck volley slipped just the right side of the post.
Bayern were on a high, but their winner was fortunate.
Makaay's cross was aimed for Ballack eight yards out, but the ball evaded the midfielder and Hedman before nestling in the net.
Bayern Munich: Kahn, Sagnol, Lizarazu (Rau 74), Kovac, Makaay,
Ze Roberto, Ballack, Pizarro, Salihamidzic (Santa Cruz 74),
Subs Not Used: Schlosser, Kuffour, Demichelis, Schweinsteiger,
Celtic: Hedman, McNamara, Balde, Varga, Agathe, Thompson,
Petrov, Lennon, Sutton, Hartson (Miller 66), Larsson.
Subs Not Used: Douglas, Gray, Sylla, Petta, Maloney, Kennedy.
Referee: Massimo De Santis (Italy).