Roy Keane scored his first Celtic goal as Gordon Strachan's side moved 10 points clear at the top of the SPL.
Keane opened the scoring with a shot from 20 yards that took a deflection on its way past keeper Allan Ferguson.
On the stroke of half-time, Bobo Balde flicked on a cross for Stephen McManus to control and score from close range.
Falkirk hit back when Kenny Milne found the top corner of the net with a fine strike after 82 minutes and Daniel McBreen missed by inches late on.
Strachan named a much-changed side, with Dion Dublin making his debut and Balde back from the African Cup of Nations.
Falkirk manager John Hughes made two changes from the side which were held by Ross County in the Scottish Cup with Alan Gow and Jean Francois Lecsinel replacing Russell Latapy and Pedro Moutinho.
Strachan happy with improvement
Celtic's Shaun Maloney passed up a glorious second-minute chance when he pulled a shot wide from 14 yards after Maciej Zurawski had pulled the ball across the face of goal.
Keane was coming in for some rough treatment from the visitors but he had the last laugh as Maloney's free-kick bounced off a defender and into his path in the 34th minute.
The former Manchester United skipper drilled a shot into the net via a deflection.
McBreen should have punished Celtic moments later when Gow picked him out unmarked in the box, but he seemed to lose sight of the ball in the floodlights and headed straight at Artur Boruc.
Celtic doubled their lead a minute before the break when a Maloney cross was flicked on by Balde and McManus chested the ball down before side-footing it into roof of the net from three yards.
Celtic looked hungry for more goals after the break and Shunsuke Nakamura sent a left-foot free-kick just past the upright from outside the area.
Hughes rues slack goals
Dublin then headed Nakamura's free-kick just over the crossbar before a Stilian Petrov header hit the turf then came off the crossbar from six yards.
Celtic were well on top but Falkirk were back in the game when Milne found the top corner of the net with a glorious strike.
And McBreen almost snatched a share of the spoils in injury time when his shot shaved the base of the post.
Celtic: Boruc, Telfer, Balde, McManus, Wilson, Nakamura (Thompson 89), Petrov, Keane, Maloney, Zurawski, Dublin. Subs Not Used: Marshall, Hartson, Varga, Pearson, Wallace, McGlinchey.
Booked: Petrov. Goals: Keane 34, McManus 44.
Falkirk: Ferguson, Cregg, Ross, Ireland, Milne, Lescinel (Moutinho 60), O'Donnell (Craig 78), Rodrigues, Thomson (Lima 85), McBreen, Gow. Subs Not Used: Howard, Latapy, Lawrie, Allison.
Booked: Ross, Lescinel, O'Donnell. Goal: Milne 83.
Att: 56,672
Ref: I Brines