Manager Ronny Delia made 10 alterations to the team that drew 1-1 at Maribor in Wednesday’s UEFA Champions League play-off first leg.
Nir Biton curled a shot against the crossbar in the first half, but the game's decisive moment arrived in the 65th minute when Eoghan O'Connell helplessly put through his own goal after Marley Watkins' cross was parried in his direction by Celtic goalkeeper Lukasz Zaluska.
The result means Inverness remain top of the fledgling Premiership table with 10 points from four games, one ahead of Hamilton Academical and Dundee United - both of whom were respective 2-1 winners over Partick Thistle and Ross County.
There was thrilling late drama at Firhill as Kallum Higginbotham gave Partick an 85th-minute lead with a spectacular long-range strike.
But joy soon turned to despair for the hosts as Tony Andreu levelled two minutes later and fellow substitute Jason Scotland pounced on an error by Conrad Balatoni to fire a last-gasp winner.
Dundee United did not endure quite such a breathless finale, but required an emphatic Chris Erskine finish four minutes from time to seal the points.
Nadir Ciftci gave the Tannadice faithful something to cheer in the 19th minute as he opened the scoring from Paul Paton's free-kick, but Jake Jervis steered home to bring County level six minutes into the second half.
Kilmarnock ensured champions Celtic will complete the weekend in fifth place as they beat Motherwell 2-0 at Rugby Park.
Youngster Robbie Muirhead rifled a magnificent opener from 25 yards and Motherwell's Fraser Kerr saw red for a high challenge on Jamie Hamill, with Sammy Clingan netting the resulting free kick.
Elsewhere, Dundee and St Johnstone were 1-0 victors over St Mirren and Aberdeen respectively. The victorious teams have six points apiece, while St Mirren - like Ross County - are yet to get off the mark.
