John Guidetti scored the only goal of the game for Celtic in the second half, latching on to an Anthony Stokes pass to slot home and send the Hoops third.
Dundee United were the day's big winners, moving top after a 3-0 win against St Mirren. Paul Paton fired in from close range as the Tangerines took the lead against the run of play before half time.
Nadir Ciftci scored on the rebound for their second after Aidan Connolly's effort was saved, and Charlie Telfer added his name to the scoresheet with his first goal for Dundee United, finishing calmly to make it three.
Across the city, Dundee fans will also be celebrating as they went to Kilmarnock and won. Hamilton left it late to rescue a point against Partick Thistle in a six-goal thriller.
Results in full: Celtic 1-0 Inverness Caledonian Thistle, Dundee United 3-0 St Mirren, Hamilton Accademical 3-3 Partick Thistle, Kilmarnock 1-3 Dundee