Falkirk captain Stephen Hetherington was also sent off for a foul in the box, leading to a nervy ending after David Goodwillie converted from the penalty spot.
Paul Sheerin named an unchanged starting eleven for the match, with Charlie Telfer placed further forward in midfield once again and the away side started on the front foot.
There was an early claim for a penalty when Clyde defender Marky Munro looked to have blocked Leon McCann’s cross with his arm after 11 minutes, but the referee played on.
Seconds later Craig McGuffie had the first effort of the match, nearly catching out Neil Parry with a dipping long range effort.
Ex-Bairn Morgaro Gomis was yellow carded for halting a Falkirk breakaway, while Charlie Telfer also received a caution for a cynical challenge on Munro.
The hosts' physicality was causing problems for the Bairns backline with David Goodwillie holding off Ben Hall in the box and nearly grabbing the opener on 23 minutes.
Mark Docherty’s deft throw found the striker in the box but he could only blast his effort straight into Paddy Martin.
Declan McDaid went close with a curling effort on 29 minutes that was saved expertly by Parry. Next to trouble the Clyde defence was Michael Ruth who hit the crossbar after his volley looked to be heading in.
The Bairns constant pressure finally paid off with the last action of the first half.
Ruth was quickest to pounce in the box when the ball was diverted back into the danger area by Parry.
The Aberdeen loanee made no mistake powering the ball into the far corner to give Falkirk the lead at the break.
Goodwillie thought he had equalised shortly after the restart when his low drive had beaten Martin, but skimmed the far post and went out of play. Target man Rob Jones should have done better with a header on 50 minutes when he found himself free at the back post, but his effort flew wide.
Steven Hetherington was cautioned taking one for the team when he halted a dangerous attack. Goodwillie’s subsequent free kick was blocked by the wall.
Telfer went close to doubling the Bairns lead on 54 minutes when his long range drive nearly snuck into the near post.
Falkirk finally doubled their advantage on 64 minutes after a brilliant solo effort from McGuffie. The winger cut inside and left the defender hopeless, giving him the space to place a curling effort in the top corner.
On 73 minutes the game was turned on its head when Hetherington was sent off after being adjudged to have brought down substitute Ross Cunningham in the box.
Goodwillie stepped up and smashed the penalty down the middle to give the Bully Wee hope.
Paul Sheerin responded by bringing on Ernaldo Krasniqi and Samuel Ompreon for wingers McGuffie and McDaid on 76 minutes.
Ompreon quickly caused the Clyde defence problems and fed in Aidan Keena who rounded Parry only to see his chipped effort go narrowly wide.
Even with ten men, the Bairns pushed forward and Dixon and Nesbitt both had chances to score after a series of corners.
Moments from the final whistle Clyde looked to have snatched a point when Goodwillie was found by Cunningham’s wicked cross, but his header flew past the post.
Paul Sheerin’s side sealed the three points in added time when Telfer found himself with an empty goal after Parry had gone up for a late corner, sending the travelling support wild.