After 88 minutes of instantly forgettable fare in Fife, second-half substitute Stewart managed to engineer space inside the Bairns area and fizz a low shot into the bottom corner.
The result takes Colin Cameron’s men out of the relegation places in the Championship standings, while Falkirk left the field to a barrage of abuse from irate visiting supporters.
That vitriol was echoed by Bairns boss Gary Holt, who said: “I want players to do what they are asked, stand up and be counted and grow a set of balls. We didn’t have that.
“It makes it easy for me selecting the team next week. And if any of those players are dropped, they can’t come complaining to me, because that is completely unacceptable.”
The overall quality of the contest was not foremost on the mind of Cameron after a hard-fought victory.
“We maybe just about deserved the win,” he said. “We are now in seventh place, just one point behind the three teams above us. Picking up the papers and seeing that gives us all a boost.”