Goals in the space of five second-half minutes from Gary Hooper (61) and Joe Ledley (66) kick-started the kind of joyous atmosphere Neil Lennon had called for ahead of the game, and Hooper's party-piece third (73) added lustre to the occasion.
Georgios Samaras smashed a late fourth (89), and the home support barely broke voice even as Aaron Doran replied for Terry Butcher's side in injury-time.
High in the stands the Hoops' suspended manager savoured a second straight title success sitting among supporters whose thoughts now turn to Hampden Park next month and the prospect of a first domestic double for six years.
Inverness' fate was a footnote to the latest chapter in Celtic's heavy history books, but defeat had an impact on the visitors' pursuit of European qualification for the first time.
The third-placed Highlanders' lead over chasing St Johnstone is now four points - with four games remaining - after Steve Lomas' side drew 2-2 with Ross County.
Caley Thistle were the last side to prevent Celtic scoring at home in an SPL game, and for an hour they promised a repeat of that November shutout as the champions-elect found it hard going.
Victor Wanyama's header - steered wide as advancing goalkeeper Antonio Reguero loomed in his eyeline - was as close as they got during a drab first half which saw a linesman's flag deny Anthony Stokes.
When Efe Ambrose missed from six yards after the break it appeared Celtic might have to settle for a point and a low-key crawl to the finishing line.
But Hooper found a route to goal through Graeme Shinnie's legs, and Ledley's controlled side-foot from a Mikael Lustig pass ended the game as a contest.
The rest was a lap of honour, Hooper's classy near-post back-flick burying Kris Commons' cross and Samaras' skill working the chance for a shot which crashed in off the bar.
Doran smuggled Inverness onto the scoresheet at the death; few in the home end even noticed.