Celtic hardly needed to move out of second gear to regain top spot in the title race.
An own goal by former Celtic player Derek Whyte and a slick finish by Stilian Petrov were enough to establish a comfortable half-time lead for the home side.
Martin O'Neill's side were happy to coast in the second half after their midweek efforts in the win over Blackburn, but still found time to add another brace through Petrov and top scorer Henrik Larsson.
Larsson threatened early on but Thistle keeper Kenny Arthur did well to block his shot.
Celtic made the breakthrough when Chris Sutton's cross from a Petrov pass was diverted past his own keeper by Whyte.
Celtic went close to increasing their lead but Sutton's volley from Scott Paterson's misdirected header was inches wide.
Another flowing move from the home team ended with Arthur gratefully clutching Alan Thompson's chip.
Thistle's only response was a looping header by Martin Hardie which keeper Robert Douglas held comfortably under his bar.
The visitors were finding it difficult just to advance into the Celtic half and fell further behind to a well-worked goal.
Neil Lennon's pass to Larsson was perfectly flicked on by the Swede to leave Petrov clear on goal and the midfield player side-footed the ball into the corner of the net.
Celtic eased up in the second half but Petrov still looked in the mood with a volley from Thompson's cross that went wide.
Arthur again denied the Celtic attack with a fingertip save from Sutton's header but was powerless to prevent Celtic's third goal.
From Sutton's pass Larsson squared to Petrov who delayed his shot before lofting the ball over the keeper.
Larsson completed the scoring with a shot after substitute David Fernandez and Shaun Maloney had combined to set up the chance