Goals from Georgios Samaras and Stephen McManus gave Celtic a comfortable victory over Falkirk.
McManus' goal in the 31st minute sparked Falkirk protests when he appeared to shoulder the ball into the net from Shunsuke Nakamura's free-kick.
Samaras added a second with a tap-in before half-time and doubled his tally in the 68th minute with a low drive.
Falkirk had a number of chances to breach the Celtic defence but failed to find a way past goalkeeper Artur Boruc.
Celtic manager Gordon Strachan had handed debuts to recent signings Marc Crosas and Glenn Loovens and both looked comfortable as the champions climbed back to the top of the Scottish Premier League table.
In the opening minute, Vennegoor of Hesselink turned inside on the right-hand edge of the box, but his curling shot flew inches wide.
Moments later, McManus almost cost Celtic a goal when he surrendered possession inside his own box and gave Falkirk's Mark Stewart the chance to pounce, but Boruc gathered.
Nakamura played a superb pass across the face of goal, but none of his team-mates could profit.
Falkirk's Scott Arfield then fired in a shot that Boruc saved.
Mark Wilson launched a powerful counter-attack down the left-hand side before thundering in a shot saved well by goalkeeper Robert Olejnik.
Vennegoor of Hesselink suffered an ankle injury in a clash with Lee Bullen and Shaun Maloney was brought on for the stricken Dutchman to make his first appearance in his second spell at the club.
The former Aston Villa man made an impact when he earned a free-kick on the right.
Nakamura curled in a beautiful ball and McManus appeared to bundle it into the back of the net with his shoulder. The goal stood, despite protests from the Falkirk players.
Michael Higdon almost levelled after 35 minutes when he forced Boruc into a superb save with a ferocious 20-yard shot.
As half-time approached, Maloney played a crucial role in Celtic's second goal when he threaded through an inch-perfect pass for Samaras and the Greek striker rounded Olejnik before slotting the ball home.
MY SPORT: DEBATE
Samaras added his second and Celtic's third in the 68th minute when Maloney picked up a long ball and back-heeled on the edge of the box for the Greek international to drive a low ball under Olejnik.
Celtic: Boruc, Hinkel, Loovens, McManus, Wilson, Nakamura, Scott Brown (Crosas 73), Hartley, McGeady, Vennegoor of Hesselink (Maloney 28), Samaras (Killen 73). Subs Not Used: Mark Brown, Robson, O'Dea, Caddis.
Booked: Scott Brown.
Goals: McManus 32, Samaras 44, 68.
Falkirk: Olejnik, Bullen, McNamara, Barr, Aafjes (Mitchell 84), John Stewart (McCaffrey 84), Cregg, McBride, Arfield, Higdon, Mark Stewart (Robertson 84). Subs Not Used: Flinders, Gibb, Staunton, Murdoch.
Booked: Mark Stewart, Cregg.
Att: 56,031
Ref: I Brines
BBC Sport Player Rater man of the match: Celtic's Shaun Maloney 8.94 (on 90 minutes).
Please note that you can still give the players marks out of 10 on BBC Sport's Player Rater after the match has finished.
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