A brace from Tony Stokes and further strikes from Liam Henderson, Stefan Johansen and Kris Commons means Celtic are Scottish champions for the 45th time.
Thistle's defence were punished for ball watching with just four minutes on the clock as Emilio Izaguirre cut inside Chris Erskine and sent a deep cross towards the back post where Stokes drifted into space and beat Paul Gallacher with a powerful header.
Substitute Henderson (49) doubled the lead minutes after coming on with a composed finish from 15 yards after Commons and Leigh Griffiths both allowed Johansen's angled ball to run to the far side of the box.
And four minutes later Johansen won a loose ball 35 yards from goal and ran on to a return pass from Griffiths to dispatch a low drive into the far corner from 12 yards.
Stokes (90) scored the goal of the game as he rifled a shot on the turn into the top corner after taking a pass from substitute Georgios Samaras.
And Samaras was involved again in stoppage-time as he carried the ball to the edge of the box and laid a pass off to Commons to shoot between Gallacher's legs.
Thistle enjoyed their best spell after the third goal and Lyle Taylor could not get enough purchase with his right boot to direct the ball between the posts from a superb Aaron Sinclair cross.
Fraser Forster then turned Gary Fraser's swerving shot from distance wide, and Taylor headed the ball straight at the Celtic keeper two minutes later.
At the other end of the pitch Commons took a wonderful pass from Stokes in his stride and tested Gallacher with a powerful low drive.
And Commons missed a late chance when he lifted the ball over the bar from inside the six-yard box after hesitation in the Thistle defence.
Moments later Christie Elliot (85) pulled a consolation goal back for Partick as he got in behind Virgil van Dijk and blasted past Forster from 20 yards.