Shaun Maloney restored Celtic's equilibrium with a goal that banished the Champions' League hangover caused by the midweek defeat at Aalborg and put daylight between them and Rangers in the title race.
The midfielder's fine first-half finish produced a 12th successive victory in the Scottish Premier League for Gordon Strachan's side, and widened the gap over their Old Firm rivals to seven points. If Celtic produced their poorest display of the season that mattered little. Strachan was able to bask in the best winning sequence of his three-and-a-half year tenure and must believe he can deliver a fourth title in a row.
Inverness contributed to a fiercely contested first half with the crisp passing that is the trademark of Craig Brewster's team and ought to have profited from a fine move in the fifth minute when Ian Black and Don Cowie cut the hosts wide open but Stephen McManus's slide snuffed out the threat.
Celtic were reliant on Andreas Hinkel to stretch the visitors and the German right-back almost broke the deadlock in the 22nd minute, bursting into the box but firing wide.
Seven minutes later Celtic went in front with a goal of true quality. Paul Hartley's tackle won possession midway in the Inverness half, he gave the ball to Shunsuke Nakamura who produced a wonderful reverse pass to Maloney who controlled the pass with his chest and spun to thrash a low right foot shot beyond goalkeeper Ryan Esson.
Georgios Samaras looked rusty after his long lay off but would have scored before half time had it not been for Grant Munro's valuable clearance from Barry Robson's cross.
Samaras was also unable to finish off a great Maloney run early in the second half and was replaced soon after by Cillian Sheridan.
When Celtic sliced chances high and wide, notably from Scott McDonald and Paul Hartley, you could see the champions settling for what they had and they edged over the finishing line without any real scare.
Strachan reflected: "To produce 12 wins in a row, shows the players can deal not only with disappointments in Europe, but also being without so many of their colleagues who are injured."