The late goal spree finally killed off a gallant challenge from John Hughes' side and the Bairns finished the game with only ten men after defender Kenny Milne's late red card.
After Scott Brown had been denied an early goal thanks to Arneu Riera's last-ditch tackle in the second minute, Falkirk stunned last term's champions by taking the lead just three minutes later.
Full-back Thomas Scobbie pushed forward on the left wing before sending in a deep cross to the far post where Michael Higdon out-jumped the static Celtic defence to send a powerful header beyond Mark Brown and into the corner of the net.
Clearly stunned by the audacity of the Bairns, the visitors responded quickly, with Jan Vennegoor of Hesselink testing fellow Dutchman Tim Krul in the Falkirk goal.
The striker's long-range effort was expertly touched round the post by the home keeper.
Krul was again called into action midway through the first half when he produced an outstanding save to deny John Kennedy, blocking a close-range header from the Celtic defender after a probing corner from Shunsuke Nakamura.
Celtic's rather fortunate equaliser arrived just before the half-hour when Massimo Donati's initial angular shot was parried by Krul before the Italian's second effort bounced off Falkirk defender Milne and over the line.
Gordon Strachan's side bombarded the Falkirk goal throughout the second half and they edged in front with 14 minutes remaining, Kenny Miller driving home after Aiden McGeady's acrobatic effort had rebounded back from the post.
Milne then received a straight red card for a professional foul on Vennegoor of Hesselink in the 78th minute and Nakamura sent the resulting free-kick past the helpless Krul to make it 3-1.
Vennegoor of Hesselink wrapped things up with a simple tap-in two minutes later as Celtic finally banished memories of last weekend's dismal goalless draw against Kilmarnock at Celtic Park.
It also brought Falkirk back down to earth after their 4-0 victory at Gretna last Saturday.