Kris Commons scored twice as Celtic all but sealed a second straight Scottish Premier League championship.
The Scotland international beat Hibernian goalkeeper Ben Williams with a strike in each half to put the hosts in command.
And Mikael Lustig converted Joe Ledley's cross to complete a comfortable win for Neil Lennon's side.
Celtic need only avoid defeat in their next league match for the title win to be declared a mathematical certainty.
Lennon's men lead Motherwell by 15 points with five matches to play and Celtic have a vastly superior goal difference.
An inviting ball into the Celtic box from Leigh Griffiths was missed by everyone and bounced just past the post as Hibs sought to make an early breakthrough.
But the home side soon took conrol and Commons gathered Gary Hooper's pass to tuck the ball past Ben Williams.
Anthony Stokes and Hooper combined to send the latter through on goal but the club's top scorer could get enough on the shot.
Commons' second owed much to poor defending as he was allowed to turn in the box and send a shot beyond Williams shortly after the break.
Celtic were playing confidence and a 25-yard strike by Anthony Stokes was beaten out by Williams.
Hat-trick-chasing Commons got the ball caught under his feet as he tried to convert a Hooper pass moments later.
Lustig had set up Commons' second and the Swede added his own name to the scoresheet just after the hour.
But Hibs players claimed unsuccessfully that Lustig had used his hand and not his head to turn the ball into the net.
Hooper headed wide shortly after news of St Mirren taking the lead against Motherwell raised excitement levels at Celtic Park.
However, a late equaliser for 'Well put the champagne on ice.