Match ends, Celtic 3, Dundee United 1.
Celtic broke through the 100-goals mark as they cruised past Dundee United on the day Neil Lennon's side were presented with the Premiership trophy.
Anthony Stokes nodded the opener before Georgios Samaras doubled the hosts' lead from the penalty spot, having been brought down by Radoslaw Cierzniak.
A Filip Twardzik own goal reduced Dundee United's deficit.
But Kris Commons restored the two-goal cushion with a fine finish following a slip by Keith Watson.
The Celtic players took to the field wearing black armbands in memory of five-year-old fan Oscar Knox, who lost his battle with cancer this week, and applause rang around the ground after five minutes as a tribute.
There was a distinct end-of-season feel to the opening exchanges, with plenty of free-flowing football on show but little threat in either final third.
Dundee United will be back at Celtic Park next week for their Scottish Cup final date with St Johnstone, and Jackie McNamara's side looked comfortable in the surroundings.
Celtic's first sight of goal fell to Leigh Griffiths from a fine Scott Brown pass, but with the ball dropping over his shoulder, the hitman produced a fresh-air swipe.
Stokes then had a dig from the edge of the box but it lacked power and United goalkeeper Cierzniak gathered easily.
At the other end Paul Paton tried his luck, curling an effort over the bar from 20 yards after tenacious play from Morgaro Gomis.
The best chance of the opening hour fell to United front man Farid El Alagui five minutes after the break.
Mark Wilson fired an effort that Fraser Forster saved, and when the ball dropped to El Alagui a few yards out, he shot over with the goal gaping.
Minutes later Griffiths had the ball in the net after latching on to Stefan Johansen's through ball, but the flag was up for offside.
United's Ryan Gauld made way for Gary Mackay-Steven on the hour and Samaras, whose Celtic deal ends this summer, came on in place of Griffiths.
And Stokes made the breakthrough after 64 minutes, netting the club's 100th league goal of the campaign.
Commons was the creator, working the ball on to his right foot and delivering to the back post where the Irishman was waiting to nod beyond Cierzniak.
Ryan Dow went off for United and his replacement, Stuart Armstrong, almost made an immediate impact. El Alagui set him free down the left with an excellent header and the midfielder cut inside before drilling in a low effort, but Forster got down brilliantly to tip it round the post.
The hosts then doubled their lead from the penalty spot.
Samaras picked Gavin Gunning's pocket in the box with a fine sliding challenge and Cierzniak hauled the Greek to the ground. The forward then got to his feet and easily beat the goalkeeper from 12 yards, netting his first league goal at Celtic Park this season.
The two-goal cushion was short-lived, though, as United got back into the game thanks to a Twardzik own goal.
Mackay-Steven was played in down the right by Armstrong and his attempted centre was diverted past Forster by the Czech.
Celtic bagged another goal immediately through Commons' delicate finish after Keith Watson slipped and gifted possession to Stokes.
Substitute Beram Kayal missed a glaring chance as Celtic poured forward in search of more goals, but it mattered little as soon the title party ensued.
- 23LustigSubstituted forKayalat 78'minutesBooked at 90mins
- 5van Dijk
- 56TwardzikSubstituted forPukkiat 84'minutes
- 28GriffithsSubstituted forSamarasat 61'minutes
- 1CierzniakBooked at 76mins
- 8RankinSubstituted forFraserat 83'minutes
- 29El Alagui
- 18DowSubstituted forArmstrongat 69'minutes
- 19GauldSubstituted forMackay-Stevenat 60'minutes
- William Collum
- Shots on Target
Second Half ends, Celtic 3, Dundee United 1.
Beram Kayal (Celtic) is shown the yellow card.
Foul by Beram Kayal (Celtic).
Stuart Armstrong (Dundee United) wins a free kick in the defensive half.
Hand ball by Beram Kayal (Celtic).
Attempt missed. Kris Commons (Celtic) right footed shot from outside the box is too high.
Scott Brown (Celtic) wins a free kick in the attacking half.
Foul by Farid El Alagui (Dundee United).
Attempt missed. Beram Kayal (Celtic) right footed shot from the centre of the box is too high.
Substitution, Celtic. Teemu Pukki replaces Filip Twardzik.
Substitution, Dundee United. Scott Fraser replaces John Rankin.
Goal! Celtic 3, Dundee United 1. Kris Commons (Celtic) left footed shot from the centre of the box to the centre of the goal. Assisted by Anthony Stokes.
Beram Kayal (Celtic) wins a free kick on the left wing.
Foul by Stuart Armstrong (Dundee United).
Own Goal by Filip Twardzik, Celtic. Celtic 2, Dundee United 1.
Substitution, Celtic. Beram Kayal replaces Mikael Lustig.
Goal! Celtic 2, Dundee United 0. Georgios Samaras (Celtic) converts the penalty with a right footed shot to the bottom right corner.
Radoslaw Cierzniak (Dundee United) is shown the yellow card.
Penalty Celtic. Georgios Samaras draws a foul in the penalty area.