Celtic established a new Scottish record of 24 consecutive league wins with a comfortable victory at Firhill.
Sutton celebrates the opening goal for Celtic
The SPL leaders spurned several early chances but took the lead after 35 minutes when Chris Sutton headed home.
Stanislav Varga headed a second goal soon after and Sutton scored from the penalty spot early in the second half.
Co-manager Gerry Britton drilled in a goal for Thistle after 55 minutes but Varga headed a simple second goal 10 minutes from time.
The visitors were on top right from the start and Thistle keeper Kenny Arthur had to make a smart save after three minutes to keep out a header from Bobo Balde.
Henrik Larsson then clipped his shot over the crossbar after being played clean through by Sutton.
The roles were reversed a few minutes later when Larsson crossed smartly with the outside of his boot but Sutton somehow skewed his header wide from six yards.
Jackie McNamara was next to try his luck and fired just wide from 20 yards following a neat Alan Thompson step-over.
The breakthrough came ten minutes before the interval when Thompson's cross was flicked on by Kennedy and headed back across goal by Larsson for Sutton to head home from five yards.
Celtic doubled their lead four minutes later with Thompson again the creator.
The Englishman floated an inviting free-kick to the back post and Varga arrived to head back across goal and into the net off the post.
Varga heads home Celtic's second goal at Firhill
James Grady had a good chance to pull his side back into the game but he fired wildly off target from close range after meeting Gerry Britton's cross at the near post.
The second half was just five minutes old when Kenny Milne foolishly barged Kennedy over in the penalty area and Sutton swept home the spot kick.
Thistle hit back in the 55th minute when Britton was first to react after Celtic keeper Robert Douglas had blocked a fierce shot from Billy Gibson.
The home side enjoyed a lot more of the ball after the goal but could not create any clear goalscoring chances.
Former Celtic favourite Jorge Cadete, who agreed a one-month deal with the Jags this week, was introduced after 64 minutes and the veteran Portuguese striker displayed a few nice touches.
The Jags were giving a much better account of themselves as the game went on but a lapse in concentration allowed Varga to score a free header from a Thompson corner in the 80th minute.
In the dying stages Cadete was given a glimpse of goal but his powerful shot was pushed away by Douglas.
Partick Thistle: Arthur, Billy Gibson, Ian Ross, Madaschi, Murray, Milne, McBride, Mitchell, Rowson, Britton, Grady. Subs: Langfield, Chiarini, Bonnes, Andy Gibson, Cadete.
Celtic: Douglas, Kennedy, Varga, Balde, McNamara, Petrov, Lennon, Pearson, Thompson, Larsson, Sutton. Subs: Marshall, Sylla, Valgaeren, Lambert, Maloney.
Referee: K Clark