It is the first time since 2004 that Celtic have won three in a row on enemy territory, adding to their two victories here last season, and they are now eight points clear of the Gers.
The closest Celtic came to a first-half opener arrived just a minute or so into the contest, as Rogic burst forward and sent a bullet strike towards the top corner for Wes Foderingham to help over.
It took some time for the Gers to grab a foothold on the match, but once they did so they enjoyed some promising moments of their own, none more so than 13 minutes in when Alfredo Morelos was sent to the ground inside the box.
The Colombian striker saw his penalty appeal turned down by referee Craig Thomson, however, and soon after Griffiths came close to curling home the opening goal for his side.
Foderingham was called into action once again late in the half to keep out Patrick Roberts after the Manchester City loanee got in behind down the right, seeing his shot saved down low at the front post.
Celtic were on top in the second half, with one Griffiths shot blocked from 10 yards out before Rogic finally found a way through from the Bhoys' sixth corner of the match.
Rangers had one big chance to equalise through Morelos, whose close-range header was stopped by Craig Gordon, and it proved to be a big moment in the match as Griffiths tucked home a second when sent clear by Roberts 65 minutes in.
The Hoops, unbeaten in league competition since May 2016, had little to trouble them in the remainder of the contest as they professionally saw things through for a sixth win from seven in the Premiership this season.