First-half goals from Joe Ledley and Charlie Mulgrew put the Hoops firmly in control, with James Forrest's 52nd-minute strike and a Fraser Wright own goal putting the gloss on an easy outing.
Chasing a top-three finish, St Johnstone were rudderless in attack and never looked like spoiling the home side's title celebrations.
Little more than one minute was on the clock when Celtic took the lead. Forrest picked up the ball to right of the area and passed across to Ledley, who rifled a shot past Alan Mannus.
Neil Lennon's side proceeded to dominate the remainder of the first half, with Gary Hooper and Anthony Stokes both going close before Mikael Lustig forced a fine save from Mannus on the half-hour.
However, Mannus was beaten for a second time on 36 minutes when Mulgrew's free-kick from the edge of the box evaded everybody and nestled in the bottom corner.
Forrest twice went close prior to the interval, his second attempt superbly tipped over by Mannus, but he made no mistake early in the second half, driving home Celtic's third after a marauding run by Hooper.
With victory assured, Celtic turned on the style. Wonderful wizardry from Stokes left the Saints defence flailing, but Forrest was unable to keep his shot down, while substitute Georgios Samaras and Hooper fluffed decent opportunities as Celtic pushed for a fourth.
Saints' miserable afternoon was complete in injury time when Fraser Wright headed Mulgrew's corner into his own net.