Celtic started the match on the front foot and they created their first opening inside the first two minutes.
Some fine interplay between Andreas Hinkel and Shunsuke Nakamura down the right flank saw the German full-back presented with the opportunity to shoot from ten yards out, but his effort was blacked and Caley cleared the danger.
Massimo Donati was the first man to trouble Caley keeper Michael Fraser, firing in a powerful 30-yard strike that the keeper could only parry.
Fraser was called into the action to make another save after 21 minutes. Aiden McGeady slid a neat ball through to Nakamura on the left flank and the wide man cut the ball back to Georgios Samaras on the edge of the area.
The big striker fired in a low right-foot effort, but he was denied by a fantastic save from Fraser, diving low to his right-hand side to push the ball clear.
Caley were largely limited to efforts on the break as Celtic dominated territorially, and it was Dougie Imrie who went closest for the visitors in the first half, firing in a low effort from the edge of the area that failed to trouble Artur Boruc as it flew wide of target.
Celtic continued to push for the opening goal as half-time approached, and Lee Naylor fired inches wide with a long-range effort before Samaras nodded wide of goal.
But the Parkhead club eventually broke the deadlock in stoppage time at the end of the first half as top scorer Scott McDonald opened the scoring, firing home his 25th goal of the season from an inswinging Nakamura free-kick.
The reigning SPL champions continued to dominate after the interval and Samaras went close at the start of the second half, heading wide of the target before firing another effort off the base of the post with the Caley keeper rooted to the spot.
Samaras eventually doubled Celtic's lead just after the hour mark, rising above the Caley defence to head home from McGeady's left-wing cross.
Caley were handed an unlikely lifeline as Celtic gifted them a goal ten minutes later. Scott Brown's loose pass at the back was pounced on by Marius Niculae who got the visitors back into the match with a fine low finish into the bottom corner past Boruc.
Caley loosened the shackles and pushed more men forward in search of an equaliser in the closing minutes. But Celtic never looked seriously troubled, and they coasted towards a deserved victory.