Celtic impressed from the outset and might have been a goal up inside 10 minutes after Scott Sinclair combined brilliantly with James Forrest, only for the playmaker to see his shot on the turn beaten away by a stretching Tomas Cerny in the Thistle goal.
The hosts were unable to keep up with Celtic's slick movement in the opening stages and Forrest should have again opened the scoring, this time as he collected a through-ball from Ntcham, before dragging his shot wide of the target.
Rodgers and his men continued to knock on the door and Thistle soon had to rely on Cerny once more, as the home stopper leapt impressively to palm away Nir Bitton's curling free kick from the edge of the box.
The breakthrough finally arrived in the 26th minute, however, as Ntcham volleyed precisely from the edge of the area, before seeing the ball take a slight deflection off Scott Brown in order to wrong-foot a stranded Cerny.
Celtic continued to dominate in the second period, although Thistle had the perfect chance to equalise when Kris Doolan broke free inside the box, only to head over the bar with only Craig Gordon to beat.
Celtic skipper Brown might have settled a few nerves late into the contest, but the midfielder saw his memorable volley into the bottom corner harshly ruled out for handball, much to the dismay of the travelling support.
Thistle might have snatched a point late on when Bitton appeared to have brought down his man inside the area, although Celtic escaped punishment before eventually going on to earn a hard-fought victory at Firhill.