It was no day for fancy football, and a game which would have been called off had it been at most other grounds.
Celtic rung the changes from the team which won at Tannadice last week, Martin O'Neill made five changes altogether.
Momo Sylla, Johan mjallby, John Kennedy and Ross Wallace all seen themselves with starting places, several players who didn't play were rested, Alan Thompson was shaking off a slight knock.
Thistle showed themselves as an attacking side, and took a surprise lead after 12 minutes, when James Grady scored his third goal against Old Firm opposition, with a header which bounced off the crossbar and into the net.
It was now important that Celtic got a goal back as soon as possible, and came out looking for that equaliser. Henrik Larsson headed just over from a Ross Wallace cross.
The equaliser came from Henrik Larsson, on 23 minutes, the King's instinct finish got the Bhoys level.
Celtic took the lead through Player of the Month, Chris Sutton. Henrik Larsson's free-kick managed to go through the wall, and Sutton's outstuck leg directed the ball home.
In the second period, the rain began to get terrential, forcing many of Celts in Rows A, B and C to head home.
Ross Wallace was impressing, and forced a superb fingertip save from the Thistle keeper midway through the second period.
Almost on the hour mark, Celtic's winner arrived. A great counter attacking move, where Larsson and Wallace exchanged one-twos, was netted home by Chris Sutton, for his second goal of the afternoon.
From then on, it was a case of waiting for the final whistle to come, Liam Miller had a chance to make it 4-1 but it wasn't to be.
We meet Thistle again on Thursday night in the CIS Cup, where a few young players are likely to play.
Celtic:
Hedman - 7
Varga - 8
Kennedy - 7
Mjallby - 7
Lennon - 8
Miller - 7
Sylla - 6 (Gray - 6)
Larsson - 7
Hartson - 6 (Petrov - 7)
Celtic-Mad Man of the Match: Neil Lennon