The Wales international is in the last few months of his contract with his future subject to much speculation but in the 39th minute of a game played in relentless rain, he showed why Hoops manager Neil Lennon is so keen to keep him by driving in from 25 yards.
The goal followed several scares from the Jags who put up a spirited performance and who will argue they deserved to leave the east end of the city with a point.
However, in the final analysis, it was the third successive win by the same score for the Hoops who extended their unbeaten league run to 19 games since the start of the season.
There was less than a minute on the clock when Jags keeper Scott Fox, who learned his trade at Celtic, tipped a Pukki header over the bar for a corner which, although it came to nothing, hinted at a long afternoon ahead for the Maryhill men.
However, far from being cowed, the visitors, who arrived on the back of a 5-1 home defeat to Motherwell, started playing with some confidence.
In the seventh minute defender Stephen O'Donnell's looping cross was met by midfielder James Craigen who headed wide from six yards under pressure from Hoops skipper Scott Brown, moments before Taylor headed a cross from Aaron Taylor-Sinclair past the far post.
In the 13th minute, after Muirhead was booked for a foul on Hoops wide-man James Forrest 25 yards from goal, Celtic's 15-goal midfielder Kris Commons stung the palms of Fox with a powerful free-kick.
However, Thistle remained dangerous on the break and moments later Parkhead keeper Fraser Forster had to dive smartly down to his left to save from Stuart Bannigan's left-footed drive.
Indeed, it looked like the Jags would surely take a shock lead in the 24th minute when Taylor- Sinclair's magnificent deep cross from the left found Christie Elliott at the back post but his diving header was blocked by Forster.
The Englishman was finding himself busier as the half unfolded but all Thistle's good work was undone when they allowed Ledley to take a pass from Efe Ambrose with enough time and space to drill a shot from 25 yards low past Fox and into the corner of the net.
The goal punctured the visitors' confidence but only momentarily and to their credit, they refused to retreat into defence.
Mulgrew had the ball in the Thistle net in the 57th minute but the offside flag was already up and moments later Fox made a fine save from a Pukki piledriver.
Doolan replaced Taylor and Lawless came on for Kallum Higginbotham, either side of double substitution for the home side, Samaras replacing Mulgrew and Stokes on for Pukki.
But there was no sudden injection of pace or excitement into a game which was in danger of petering out in almost silence.
Thistle kept trying to break forward for the leveller and in the 85th minute, following a corner which the Hoops failed to clear properly, Lawless' shot went through a crowd of players before being cleared at the post by right-back Adam Matthews.
Christie then failed to get enough on a header moments later to end the brief spell of pressure on the Celtic goal.
No one could have begrudged the Jags a share of the spoils but once again they found themselves short of end product while Celtic, despite not being at their best, march on towards the title.
- Sports & Recreation
- Charlie Mulgrew
- Neil Lennon