Thistle, under caretaker manager John Lambie, went close in the fifth minute when Ken Milne's 25-yard shot flew just past the far post.
However, the same player contributed to Falkirk taking the lead 60 seconds later when his attempted cross-field pass was blocked by John O'Neil and the loose ball fell kindly to Darryl Duffy who ran through unopposed before firing low past Kenny Arthur.
Falkirk's lead only lasted for two minutes. When a corner was not dealt with by keeper Allan Ferguson, the loose ball was tapped home from close range by Armand One.
Both sides were keen to take the lead with Falkirk's Russell Latapy going close on 22 and 30 minutes. His first free-kick flashed wide and his second was brilliantly saved by Arthur in the Jags goal.
Thistle hit back, and on 32 minutes One's turn and cross was cleared by Kevin James and four minutes later Andy McLaren's 22-yard shot was parried and then cleared by Ferguson.
The second half started with Thistle on the attack, and One had three chances to score but the Falkirk defence proved equal to his efforts.
Falkirk hit back and, on 53 minutes, their sustained pressure ended with Duffy's 15-yard shot seeming goalbound until Milne somehow managed to clear the effort off the line.
Undaunted, Falkirk continued to press, with the ever-dangerous Duffy, setting up O'Neil and Daniel McBreen just before the hour, but both shots flashed high and wide.
Thistle's winner came on the hour, when Juan Ramon Escalas sent One clear and he made no mistake with an 18-yard thunderbolt that gave Ferguson no chance.
Falkirk were unable to mount any further attacks and it was Thistle who finished the game strongly with Derek Fleming shooting over on 70 minutes. A minute later his pass found Adam Strachan and the youngster ran a full 30 yards only to see his shot well-saved by Ferguson.
The full-time whistle was greeted by cheers from the home supporters as the Jags secured a much-needed and well-deserved victory.