The striker's double - as well as efforts from Scott Sinclair and Callum McGregor - ensured that it was an easy afternoon for the defending champions, who allowed Hearts a late consolation goal from Esmael Goncalves.
It took just four minutes for Celtic to create their first opportunity of the match, but Nir Bitton failed to hit the target with a header at the back post after meeting Griffiths's corner.
Twice in the space of two minutes, Griffiths would have felt that he should have scored but after being denied by goalkeeper Jack Hamilton, he sliced an effort wide of the near post.
However, his persistence paid off just before the half-hour mark as he gave Celtic the lead from close range after holding off challenges from both Rafal Grzelak and Hamilton.
Before the break, James Forrest saw a shot towards the near post saved by Hamilton, before Callum McGregor directed an attempt marginally wide of the far post after being teed up by a clever flick from Scott Brown.
Soon after the restart, Celtic doubled their advantage through Sinclair, who was in the right place at the right time to convert from just two yards out after Aaron Hughes had sliced a clearance into his path.
The game was effectively over as a contest and Celtic used the situation to throw more players forward in search of goals, with McGregor twice going close with long-range efforts.
However, McGregor soon turned provider for Griffiths's second, with the 24-year-old's cutback being headed into the net from close range by his teammate.
McGregor managed to get himself onto the scoresheet with 17 minutes remaining after a surging run from Sinclair ended with a pass to the Scottish international, who lashed the ball into the roof of the net from 20 yards.
Celtic were coasting at this stage, but they gifted Hearts a consolation goal with six minutes left when Goncalves's shot from an acute angle found the roof of the net via the body of Gordon.
Brendan Rodgers will be disappointed with the lack of clean sheet on a routine afternoon for his side, but the Northern Irishman will be delighted with the performances from his attacking players, who probably should have added more goals in a one-sided match.