An Aiden McGeady hat-trick earned Celtic their first win in four games as they stretched their lead at the top of the Clydesdale Bank Premier League to five points.
Scott McDonald netted an early penalty at a sparsely-populated Celtic Park and McGeady struck against the run of play just before the break.
Falkirk's comeback hopes were punctured when Darren Barr was sent off in the 63rd minute and McGeady soon killed them off with two clinical finishes.
Falkirk went into the game as the form team after scoring eight goals in wins over St Mirren and Dundee United, while Celtic had sandwiched defeat by AC Milan with draws against Hearts and Saints.
Gordon Strachan handed 20-year-old left-back Ryan Conroy a start while Massimo Donati returned from injury as Darren O'Dea and Jiri Jarosik dropped to the bench alongside Derek Riordan, who failed to get any action despite his late equaliser against St Mirren.
Despite an official attendance of 54,291, which included no-show season-ticket holders, Celtic Park looked less than half full.
But the hosts started strongly and McDonald atoned for an overhit cross towards the unmarked Jan Vennegoor of Hesselink when he won and converted a ninth-minute penalty.
The Australian collected a clever pass from McGeady and sprinted forward before he was needlessly brought down by Kenny Milne just inside the left edge of the box. The former Motherwell striker sent Tim Krul the wrong way to net his 16th goal of the season.
McDonald soon headed badly off target from a McGeady cross and Krul pushed away Gary Caldwell's powerful low shot.
Dean Holden blocked from Scott Brown from ten yards following a blocked shot by McGeady, who could easily have gone down under a rash penalty-box challenge.
But Falkirk recovered and twice had efforts cleared off the line.
Scott Arfield should have levelled after Mark Brown palmed Pedro Moutinho's low effort, but Caldwell produced a tremendous block on the line.
And Conroy cleared after the Hoops keeper got a slight touch on a Gerard Aafjes header following Moutinho's corner.
Falkirk appealed for a penalty after the ball struck the full-back on his upper body but Dougie McDonald waved play on.
The visitors continued to press and Moutinho shot just over from 25 yards before Stephen McManus was booked for taking out Michael Higdon as Falkirk embarked on a promising counter.
Higdon volleyed at Brown before Vennegoor of Hesselink was booked for persistent fouling as the hosts grew frustrated.
However, McGeady grabbed Celtic's second in the 41st minute when the unmarked winger collected McDonald's cutback 15 yards out and fired a left-footed shot in off the post.
Vennegoor of Hesselink thought he had scored moments after the restart when he headed McGeady's back-post cross past Krul but Milne blocked right on the line.
Falkirk, with a three-pronged forward line, continued to move forward quickly and Brown saved long-range shots from Graham Barrett and Arfield.
Celtic responded and McDonald forced Krul to block at his near post after good wing play from Conroy and the Dutch keeper scrambled to save Donati's 20-yard drive.
And Falkirk's chances evaporated in the 63rd minute when Barr - who had been booked seconds before the break for a foul on Vennegoor of Hesselink - received a second yellow card for hauling back McGeady.
Celtic went for the kill and, after Paul Hartley had struck the bar with a thunderous 20-yard strike, McGeady cut across from the left and curled a right-footed effort into the corner with 23 minutes remaining.
Vennegoor of Hesselink volleyed into the side netting from a tight angle but Celtic appeared to ease off as Strachan brought on O'Dea and Killen.
However, McGeady rounded off his impressive display in the 82nd minute by slipping the ball past the onrushing Krul with his left foot after McDonald had spotted his bursting run on the break.
