The substitute tapped in an 86th minute winner after Falkirk had done everything but beat inspired Sons stopper Alan Martin in an entertaining, if nerve-shredding, match for the 4,200 strong home support.
The Bairns were improved on recent showings, Myles Hippolyte particularly impressed starting the match but Dumbarton gave the Bairns a few early scares before Peter Houston's side really took control of the first half.
Robert Thomson took advantage of Danny Rogers dropping a cross on landing on the ground and shot at goal on 4 minutes, but Luca Gasparotto was on-hand to tap off the line.
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Rogers also saw a shot from Ryan Stevenson, on the turn, skim inches wide of his left-hand post just a few minutes later.
The Bairns though took the game to the visitors after this and Stevie Aitken's side barely threatened, nor did they look likely too for the remainder of the half.
They had goalkeeper Alan Martin to tahnk for keeping the score down and blank at half-time with two excellent saves to deny first John Baird with a point blank shot from three yards and then a Myles Hioppolyte diving header from a similar distance which the ex-Scotland goalkeeper clawed off the goal-line.
Falkirk's wide play -- particularly from Hippolyte -- and deliveries were good but there was often little height to take advantage of the crosses. Luke Leahy came close but failed to connect with a Lewis Kidd cross but the scores remained blank and equal at the break.
The opening to the second half followed the pattern of the first with a scare for the Bairns. Luca Gasparotto played a pass back to Rogers and the keeper slipped as he connected with the ball and his kick went straight to Ryan Stevenson. The ex-Hearts and Partick Thistle player rushed his shot however, and took it first time and screwed it well wide.
Josh Todd then had a one-on-one with Rogers after a break up the park but Danny Rogers stood tall to block.
The Bairns immediately raced up the field and John Baird did well to shuffle down the by-line and cut-back into a dangerous area front and centre of goal but there were no takers. Tom Taiwo rushed in from deep in the midfield but pulled his effort wide.
The Bairns went even closer when Leahy headed a Sibbald free-kick off the top off the crossbar and John Baird miscued a Hippolyte cross and scooped it well over. The busy little striker who hasn't scored competitively in 15 games was replaced by Lee Miller and it proved an inspired change as Miller came to the Bairns rescue four minutes from time.