Two goals from Kris Commons and a Mikael Lustig finish gave Neil Lennon's side a thoroughly deserved victory at Celtic Park.
But second-placed Motherwell's 2-2 draw with St Mirren put the Bhoys' celebrations on hold for at least a fortnight.
However, with Stuart McCall's side trailing the leaders by 15 points with five games remaining after the split and having a vastly inferior goal difference, Celtic are all but assured a 44th SPL crown.
Hibs had beaten Celtic in both their previous encounters this season and were the first to threaten at Celtic Park, but Leigh Griffiths' free-kick was missed by everyone before skipping past Fraser Forster's far post.
After that, the home side took control of the game as Commons drove them in front following a neat lay-off from Gary Hooper.
Hooper could have doubled the Hoops lead after breaking through the away defence to take a return pass from Anthony Stokes but his finish lacked power and was easily saved.
Celtic's dominance continued but it took until early in the second half for them to increase their lead.
Victor Wanyama played the ball to the supporting Lustig and when his cut-back found Commons he turned smartly and found the net with a convincing finish.
Lustig made it 3-0 just after the hour mark, converting Joe Ledley's cross with his head. The Hibs players claimed the ball came off his arm on the way through but the strike stood.
As news began to filter through that Motherwell were losing 2-1 at home to St Mirren the party began at Celtic Park, but James McFadden's late equaliser for Stuart McCall's side meant the champagne had to be put back on ice.