Stokes netted a hat-trick and set up another for Leigh Griffiths before Efe Ambrose and Teemu Pukki both scored inside the same minute.
It took Celtic until nine minutes before the interval to make the breakthrough, when Stokes lost his marker inside the penalty area and powered his downward header past Dean Brill.
The visitors were undone again on 45 minutes when Kris Commons allowed a cut-back from Griffiths to run to Stokes and the Irishman applied the finish with a crisp shot.
And Stokes (54) completed his treble when he sent keeper Brill the wrong way from the penalty spot moments after Gary Warren had upended Stefan Johansen when the midfielder pounced on a poor defensive pass.
Stokes turned provider on 68 minutes as he rolled the ball into the path of Griffiths and he curled a shot into the corner.
Ambrose got on the end of an inswinging cross from Commons 12 minutes from time to head past the keeper, and followed the goal with his trademark acrobatics.
Substitute Pukki showed great composure 40 seconds later to dispatch the ball across Brill into the far corner of the net.
Commons was denied an opening goal on 15 minutes when Brill turned his low net-bound shot round the post for a corner.
Three minutes after the opening goal Brill dived down to turn away a powerful Stokes drive from 25 yards, after the Celtic striker had shown some neat footwork.
The Caley Thistle keeper was back in action moments later when he diverted a fierce shot from Adam Mathews round the post with his left hand.
Celtic continued to apply the pressure after the break and Brill was quickly back in action as he tipped a Griffith shot over the crossbar.
Referee Craig Charleston awarded Inverness a penalty within 60 seconds of Celtic's third goal as Billy McKay appeared to bump into Virgil van Dijk, but Aaron Doran's spot-kick was saved by Fraser Forster.
Stokes was denied a fourth goal when his shot smacked the bar and when the ball was retuned across the face of goal van Dijk hit the post with his header.