Gordon Strachan's men simply had too much for their plucky opponents who enjoyed some neat possession throughout.
John Hughes and his side have won admirers for their passing football despite their lowly position and they opened this game positively.
Within eight minutes they had created two half-chances, firstly through Carl Finnigan's 18-yard shot on four minutes that Artur Boruc held.
They went even closer through Michael Higdon's eighth-minute drive from the edge of the box which scraped the bar after a clever one-two with Scott Arfield.
Both sides were forced into early changes through injury with Georgios Samaras being replaced by Jan Vennegoor of Hesselink while Falkirk's Steven Pressley made way for Lee Bullen.
Dani Mallo punched clear from an 11th-minute Shunsuke Nakamura corner as Celtic at last came alive. Falkirk still pressed but they lacked menace around the box.
Celtic went in front just before the half-hour mark when Gary Caldwell tapped home Nakamura's excellent free-kick.
Falkirk bounced back and looked dangerous from a couple of Neil McCann corners. However, the champions finished the first half at a very high tempo and twice struck the woodwork.
Firstly, Stephen McManus headed on to the bar from a Nakamura free-kick and then, in first-half stoppage time, the same two players combined with the Celtic skipper again out of luck as the woodwork came to Falkirk's rescue for a second time.
Despite a determined start to the second half by the visitors, Celtic claimed the crucial second goal on 62 minutes when Vennegoor of Hesselink tapped home from an exquisite Nakamura cross.
Again Falkirk rallied and both Arfield and Finnigan forced saves from Boruc.
However, the Bhoys sealed the three points in stunning fashion 12 minutes from time when playmaker Aiden McGeady rifled home a 25-yard drive.
Celtic added a fourth goal in stoppage time when Republic of Ireland defender Darren O'Dea nodded home from close range after McManus had caught out Mallo with a pinpoint cross.
Celtic will reflect on a job well done while Falkirk showed signs that they can stay in the SPL if they can only produce an end product to some of their neat outfield play.