In a dress rehearsal of next Sunday's Scottish Cup semi-final, Leigh Griffiths controlled Scott Brown's long ball to give Ronny Deila's league leaders a third minute advantage.
Celtic were in front for less than a minute, though, as Edward Ofere pounced from close range.
Inverness suffered a setback when goalkeeper Dean Brill left the field on a stretcher due to a dislocated knee, although replacement Ryan Esson excelled to deny Efe Ambrose and Jason Denayer.
Celtic are eight points clear of Aberdeen, with the second-placed team taking on Kilmarnock on Sunday, while Inverness are 10 points further back in third.
Caley are six points better off than Dundee United, who were 1-0 winners over Hamilton Academical.
Chris Erskine's 70th-minute drive ended a run of 10 games without a win for United and denied Hamilton a top-six finish.
A Hamilton win would have dumped Dundee out of the top six after they lost by the same scoreline at fifth-placed St Johnstone.
Brian Graham netted a curling winner after 26 minutes, while David Clarkson hit the post for Dundee, who could still be overhauled in sixth by Kilmarnock if they lose to Celtic later this month and Gary Locke's side secure the necessary goal difference swing, alongside wins in their 32nd and 33rd league fixtures of the campaign.
Lyle Taylor notched a second-half brace as Partick Thistle ended Motherwell's recent revival with a 2-0 win.
