Thistle’s Stephen O’Donnell was the driving force in the first half and created the opening goal in 24 minutes.
O’Donnell sped past Murray Wallace and crossed low where Paul Cairney flicked on for Mark McGuigan to sweep the ball home from four yards out.
Falkirk pressed to get back level in the second half and Farid El Alagui had a shot deflected wide on the hour mark before heading past the far post from the resultant corner.
Jay Fulton was not far away with a drive from 25 yards after El Alagui had chested the ball into his path and they finally drew level just seconds after substitute Kris Faulds had cleared a Conrad Balatoni header off the line following a Thistle corner.
The Bairns broke up the park and Craig Sibbald crossed from the left for Alston and he finished in fine style from 16 yards.