Second-half goals by Georgios Samaras, Koki Mizuno and Scott McDonald rather flattered the champions as they had to work hard for the three points.
Mizuno and McDonald struck in the closing minutes to complete an unhappy afternoon for the home side.
Falkirk hit the post late on as they tried to salvage a point but Celtic held firm and eventually stretched away for an important win.
McDonald tested Robert Olejnik after only two minutes but the goalkeeper was well positioned to beat out his shot.
Celtic started strongly and had Falkirk under the cosh but the home side weathered the storm and put Celtic under some pressure themselves.
A mistake by Mizuno gave Scott Arfield an opening but Glenn Loovens managed to block the ball before Artur Boruc was troubled.
Samaras then had a chance after good work from McDonald but he was just inches away from opening the scoring with his well-struck shot.
But it was Falkirk that came closest to breaking the deadlock in the first half. Arfield sent Steve Lovell clear and he stabbed the ball past Boruc only to see the alert Darren O'Dea handily placed to clear the ball off the line.
Celtic responded immediately with McDonald going close with a head-flick after a measured cross from Andreas Hinkel.
Hinkel was causing Falkirk some problems and he created another chance for the Australian striker with a strong run but McDonald again sent his effort wide.
Samaras should have given Celtic a half-time lead after McDonald laid the ball into his path but Olejnik spread himself well to save.
Neil McCann had a chance for Falkirk on the stroke of half-time but could get no power in his shot and Boruc collected comfortably.
Celtic made the breakthrough three minutes into the second half after Olejnik had carelessly given away a throw-in. McDonald collected the ball and supplied the cross for Samaras to score with a fine diving header.
Mizuno then chased what appeared to be a lost cause to retrieve the ball in the wind and his cross picked out Samaras but he could not steer his header on target.
The Japanese player was starting to make his mark and he set up a chance for McDonald but his final shot was tame and Olejnik saved easily.
Mizuno gave Samaras an opportunity in the 73rd minute as Celtic produced a great counter-attack but the Greek striker's shot was marginally off-target.
There was an escape for Celtic three minutes later when Bairns substitute Mark Stewart tried his luck with a 25-yard shot which struck the post with Boruc beaten.
But Mizuno eased any fears with a classy finish in the 90th minute after being sent clear by compatriot Shunsuke Nakamura.
McDonald then rounded off the scoring deep into stoppage time when he took the ball round Olejnik to net.