It was a poor performance from Celtic in the teatime kick-off, missing the chance to go top with their much talked-about game in hand.
It leaves the Hoops one point behind Rangers in the title race, with two of their three remaining games away from home.
It also means the title could go down to the final day of the season.
Rangers play Hearts at Ibrox on Saturday lunchtime in a game they almost always win. Celtic play away to Kilmarnock 24 hours later.
Then Rangers play Dundee United at Ibrox next Tuesday before Celtic travel away again – this time to meet Hearts at Tynecastle next Wednesday.
The Hoops finally play at home again on the last day of the season on Sunday week against Motherwell while Rangers travel to Kilmarnock on the same day – again Rangers almost always win at Rugby Park.
Tonight’s shocker at Inverness got off to an awful start for Celtic.
Adam Rooney’s chip on seven minutes gave the hosts the lead, but a superb Kris Commons strike from 18 yards out two minutes later restored the balance.
Grant Munro’s screamer restored Caley’s lead on 53 minutes, then Shane Sutherland fired home for the third.
Commons converted for Celtic from the spot when Shaun Maloney was felled in stoppage time, but it came too late.
Paddy McCourt had a late shout for a penalty waved away by the referee.
But it would have been an undeserved point – ICT were the better team.
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