Stewart latched on to goalkeeper David Hay's goal-kick before converting from 12 yards for the only goal of the game.
Archie Campbell and Kyle Miller had chances to make it 2-0 before Thistle sub Shaun Fraser had a shot saved.
Partick Thistle: Fox, Paton, Robertson, Archibald, Boyle, McGowan, McNamara (Campbell 66), Rowson, Erskine (Fraser 66), Doolan, Grehan (Flannigan 56). Subs Not Used: Scully, Balatoni.
Cowdenbeath: Hay, Baxter, Winter, Adamson, Vauls, Miller, Makel (McKenzie 72), Ramsay, Robertson, Stewart (Crawford 90), Campbell. Subs Not Used: Roy, Coult, Byren.
Booked: Campbell, Winter.
Goals: Stewart 50.
Attendance: 1,754
Referee: Steven McLean
Source: BBC Sport
Source: BBC Sport