Tony Stokes, Georgios Samaras, and Kris Commons netted in the second half at Celtic Park, while an own goal from Filip Twardzik gave the Scottish Cup finalists a consolation.
The Hoops hit their 100th league goal of the season when Commons turned Sean Dillon inside out and crossed for Stokes to beat Radoslaw Cierzniak with a downward header from six yards.
Samaras signed off his Celtic career when he slid in to rob Gavin Gunning inside the box before he was tripped by Cierzniak, seconds before the Greece international dispatched the resulting penalty with ease on 76 minutes.
United rallied three minutes later when Stuart Armstrong threaded a pass through to Gary Mackay-Steven and his cut-back came off Twardzik and deflected past Fraser Forster.
But Celtic restored their two-goal advantage when United defender Keith Watson slipped and Stokes rolled a pass in front of Commons who dinked the ball past Cierzniak.
United had an escape when Cierzniak drifted towards the side of his box to cut out a through pass to Leigh Griffiths, but the striker got to the ball first and forced the United keeper to dive to his right and divert the net-bound shot round for a corner.
With half-an-hour on the clock Stokes stepped inside Wilson and sent a daisy cutter towards the left corner but Cierzniak got down to make a comfortable stop moments before he saved a firm drive from Griffiths at his near post.
United eventually had an effort at goal three minutes before the break when Morgaro Gomis and Ryan Gauld combined to set up Paul Paton but his curling shot drifted over the bar.
Six minutes after the interval United should have taken the lead when former Celtic defender Wilson worked a corner with Ryan Dow then moved into the Hoops box before unleashing a shot which Forster could only parry to the feet of Farid El Alagui but he managed to knock the ball over from a couple of yards out.
That escape appeared to shake Celtic out of their slumber. Griffiths had the ball in the net two minutes later but the flag was up for an infringement.
Commons again caused consternation in the United ranks shortly after the opening goal when he jinked into space just outside the penalty area and forced Cierzniak into action to deal with his powerful drive.
At the other end, United substitute Armstrong cut inside Efe Ambrose and tried to beat Forster at his near post, but the England international got down to turn the ball round for a corner.
Beram Kayal sliced a glorious chance wide with just the keeper to beat in the dying minutes, but the points had been secured by then.