The Highlanders had held the Hoops on their last two clashes at the Caledonian Stadium and were keen to cause the champions problems again.
Inverness were dealt an early blow in the very first minute when Dennis Wyness dislocated his shoulder and was replaced by young Rory McAllister.
Celtic settled quickly and Vennegoor of Hesselink volleyed wide early on when he met a Lee Naylor cross.
McAllister then forced a decent save from keeper Artur Boruc when he had a crack from the edge of the penalty box.
There were few clear-cut chances for the bulk of the first half but McAllister and John Rankin went close from distance as the hosts upped the pace.
Then Celtic snatched the lead from nowhere when a blunder by Roy McBain saw him miscue a shot against the bar and Derek Riordan was on hand to fire his side in front on 37 minutes.
Steven Pressley had to go off for the Hoops when he picked up a knock and Darren O'Dea took his place.
Inverness were denied a spot-kick when referee Iain Brines refused to award a penalty when McBain was felled by Stephen McManus.
Inverness finished the half strongly but could not find a leveller.
They did start the second period in a positive manner and Barry Wilson's shot was spilled by Boruc, but McBain's follow-up was blocked by McManus.
Graham Bayne squared the match when his stooping header from a Rankin cross beat the keeper.
But just as time was running out, Venegoor of Hesselink punished a poor clearance from Darren Dods and netted the last-gasp winner.
His afternoon was spoiled though when the referee flashed a second yellow card for his celebration with the supporters.
The result puts the champions an awesome 19 points clear at the summit of the SPL table.