There was almost nothing in Milan's dreary display to suggest that they will go any further than last season when they were dispatched by Barcelona after a campaign which featured a home defeat by Zenit St Petersburg and draws with Malaga and Anderlecht.
With Barcelona and Ajax Amsterdam completing Group H, the seven-times champions might not even get that far this time.
Only Celtic's lack of composure and belief in the last third of the field prevented the Scottish champions from leaving San Siro with a memorable win against opponents who were barely able to string two passes together.
Milan's performance was summed up midway through the second half when Mario Balotelli fired a free kick into the Celtic wall and the ball fell to team mate Nigel de Jong, who contrived to lose possession.
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Celtic nearly took the lead in the 80h minute when Anthony Stokes's curling 30-metre free kick bounced off the Milan bar with Christian Abbiati beaten, yet within six minutes found themselves two goals behind.
HARMLESSLY WIDE
Milan got their break when Colombia defender Cristian Zapata's low shot, which was heading harmlessly wide, was deflected into the net by hapless defender Emilio Izaguirre in the 82nd minute.
Four minutes later, Balotelli, who had been ineffectual all night from free kicks, finally found the target and goalkeeper Fraser Forster parried the ball into the mouth of the goal where Ghana midfielder Muntari headed it over the line.
"We dominated the game for long periods," Celtic manager Neil Lennon told reporters. "I said to the players that when you are on top you need to take your chances. I thought we were brilliant. Sometimes in football you don't get what you deserve."
Milan midfielder Nigel de Jong admitted it was a poor display.
"It was a lucky win but sometimes you need some luck," said the Dutchman. "I do not think we started off very well. We let Celtic dictate in the first half. It is a very important result."
Milan, who have taken four points from their opening three league games, were missing injured trio Stephan El Shaarawy, Kaka and Riccardo Montolivo but nearly all their starting line-up had international experience and looked good enough on paper to cruise to a win.
Instead, they were shaky at the back and devoid of creativity in midfielder while Balotelli and new signing Alessandro Matri never struck up an understanding in attack.
Balotelli spent much of the match looking out of sorts and complaining when he was not given free kicks
Milan created a couple of openings in a promising opening 10 minutes but after that were restricted to long-range efforts.
Celtic more than matched them and could have gone ahead when Charlie Mulgrew's indirect free kick from 10 metres was charged down midway through the first half.
Giorgos Samaras nearly put Celtic ahead early in the second half when he bursts forward and his powerful drive curled away from the post at the last minute.
"At the end, it's the win that counts," said Milan coach Massimiliano Allegri, who has spent much of his three years at Milan fighting speculation that he could be dismissed.
"We suffered a bit, especially in the second half...and the goal was a bit lucky, but it was a good win."
(Writing by Brian Homewood in Berne; Editing by Ed Osmond)
(Reporting by Brian Homewood)
