The champions were forced to toil throughout a goalless first half, and Craig Gordon - who was making his first competitive start in more than two years - had to push away Steven MacLean's shot in the 20th minute.
The Bhoys did manage to forge a few chances for themselves in the opening 45 minutes, however. First, Anthony Stokes curled a 25-yard free kick just wide before Callum McGregor tested Alan Mannus with a low shot.
Kris Commons saw much of the ball for Celtic, but he was unable to put his side ahead as he pulled a shot wide of the near post shortly before the half-time whistle sounded.
Commons was the architect of many Celtic goals last season and it proved to be the case again this evening with the opener. The midfielder dispossessed Steven Anderson and fed Stokes, who rounded the goalkeeper before slotting the ball home.
McGregor waltzed through the home defence before blazing over in the 84th minute, but just 60 seconds later he sent another shot towards goal, which crept under Mannus and ensured Deila's first league game in charge of Celtic ended in victory.