Celtic 2 Falkirk 1
An added bonus for the home side was Roy Keane opening his account before Stephen McManus made it 2-0 just before half-time.
However a goal seven minutes from time by Kenny Milne caused panic in the Celtic defence and if Daniel McBreen's shot had been inches more accurate near the end, Falkirk may well have snatched an unlikely draw.
Celtic nearly took an early lead when Shaun Maloney's drive went narrowly wide from Maciej Zurawski's cut back.
Dion Dublin was making his debut and won most of his challenges in the air without creating too much threat.
Keane made the breakthrough when Maloney's cross was only partially cleared, and from 20 yards the midfielder's strike took a slight deflection on its way into the net.
Celtic added to their lead when McManus lashed home his shot after Dublin's clever touch from Maloney's cross set up the chance.
The home team spurned many chances to finish off the game, though Zurawski was unfortunate to see his effort come back off the bar.
Falkirk reduced the deficit when substitute Liam Craig's cross was cleverly laid back by Pedro Moutinho to Milne, whose shot from 18 yards gave Artur Boruc no chance.
Any composure in the home defence had by now disappeared and Boruc made a good save from Alan Gow, before McBreen's shot on the turn drifted narrowly wide with the keeper beaten.