Leigh Griffiths, Scott Brown, Kris Commons, James Forrest and Nir Bitton all scored on an emphatic night for Ronny Deila’s side, who are one game away from a fourth successive SPFL trophy.
The win – Celtic’s third in a row – means the Glasgow side could be champions on Saturday evening should second-place Aberdeen fail to beat Dundee United at Tannadice.
Or they could clinch the title with victory in their next game at Aberdeen on Sunday May 10.
Griffiths’ 19th goal of the season and 15th since the turn of the year opened the scoring; the striker leaping above Dees defender Thomas Konrad to meet Emilio Izaguirre’s cross and head home powerfully past Scott Bain.
And Commons played in Brown, who barely broke stride before knocking the ball low into the far corner, to give the hosts a 2-0 half-time lead.
Substitute Darnell Fisher was brought down by Paul McGinn on 65 minutes allowing Commons to confidently stroke home the third before setting up Forrest for a well-taken fourth
Bitton slammed in the fifth from long range with two minutes remaining.