Kris Commons added the second as the champions made light of their long-haul European travels, carrying too much attacking potency for the defensively-minded hosts to record their 14th straight win over their Glasgow rivals.
Celtic made a bright start with Leigh Griffiths in the thick of it, the striker – back in for the suspended Nadir Ciftci – bulleting a header over the bar from 10 yards from Emilio Izaguirre’s swinging cross before working Tomas Cerny with a 20-yard free-kick.
Commoms was also looking lively, firing at Cerny from 16 yards after working space in the area, but the visitors were forced into an early substitution when Stuart Armstrong came off to be replaced by Callum McGregor.
The change did little to alter the pattern of play as Thistle scrambled clear as Griffiths threatened, Virgil van Dijk sent a daisy-cutter thudding off the base of the post from 30 yards and Rogic screwed wide from 18 yards when well placed.
But the pressure had to tell and the breakthrough duly arrived as Rogic (28) flicked home from 12 yards having been teed up by Griffiths.
Craig Gordon had rarely been troubled but would have had a flutter of anxiety when Thistle appealed for a penalty after David Wilson had volleyed the ball into Mikael Lustig’s arm but the referee deemed the handball to be accidental.
Thistle’s first-half display had been largely passive but they began the second period with renewed vigour, their optimism enhanced by the introducion of Mathias Pogba off the bench.
Callum Booth dragged his shot across the face but any hope of a Thistle revival were quashed as Commons (63) did well to cushion Nir Bitton’s long pass before flicking his shot over the on-rushing Cerny.
The Thistle keeper beat away a fierce Griffiths’ drive but Van Dijk had to be on his toes to clear Booth’s driven cross at the other end with Pogba lurking.
Pogba blazed wildly over in the final stages and went closer from 10 yards following a galloping run by David Amoo but there was to be no consolation for the new signing – or the long-suffering home support.