The Bairns were able to net twice but found themselves being constantly thwarted by their former keeper David Mitchell in the Clyde goal who made several excellent saves throughout the match.
One upside from the day is that Raith suffered a 1-0 defeat at Dumbarton while Airdire lost 1-0 at Montrose meaning there was no change at the top of the League 1 table other than East Fife making up ground on the top three with a win over Forfar.
With top scorer Declan McManus suspended it was David McMillan who started up front with Conor Sammon while Charlie Telfer replaced the injured Josh Todd in the only other change from last weekend's 1-0 win over Montrose.
The game got off to the worst possible start from a Falkirk point of view as they went 1-0 down after just four minutes.
A mix up at the back allowed Mark Lamont through on goal and he made no mistakes while one-on-one with Robbie Mutch as he coolly slid the ball past the Bairns' stopper with a side footed finish.
Clyde should have gone 2-0 up five minutes later when good counter attacking play saw Ross Cunningham, Ally Love and Chris McStay link up well with the latter getting the ball inside the box in yards of space but Mutch came flying off his line to block the shot at McStay's feet.
The next 20 minutes were a back and forth contest with both teams creating chances which were either wide or comfortably held by the respective keepers with the biggest chance coming as David Mitchell collided with one of his own players as he came to collect a cross and the ball went goalwards but Martin McNiff got back to scoop it off the line.
Then on 40 minutes it was 2-0 to Clyde when a long ball over the top for David Goodwillie saw Robbie Mutch come out to try and beat him to it but he took the striker out on the edge of the box and referee David Dickinson pointed to the spot.
Mutch escaped with only a yellow as enough Falkirk players made it back to defend the goal and prevent it being a clear goalscoring opportunity.
Goodwillie stepped up to take the penalty and didn't look anything like a striker who had went five games without a goal as he calmly dinked it in to the net sending Mutch the wrong way.
Falkirk were thrown a lifeline before half time though when Tom Lang brought down Charlie Telfer inside the penalty are on 44 minutes and the Bairns had a penalty of their own.
Telfer himself stepped up to take it and, although Mitchell went the right way, it was right in to the corner of the net to make it 2-1 at the break.
The pivotal moment of the game came early in the second half as Mitchell pulled off two outstanding saves to prevent Falkirk equalising,
Firstly he blocked a Sammon shot after McMillan had played him in before the ball eventually fell to Aidan Connolly who got a shot away but Mitchell managed to dive across goal and block it our for a corner.
From the resulting corner kick Ben Hall got a strong header on the end of it but Mitchell did brilliantly to tip it on to the cross bar before the Clyde defence eventually cleared.
Clyde then made it 3-1 on 51 minutes when a Lamont shot was blocked by Mutch but the ball fell to Ally Love who managed to get it to David Goodwille who stabbed it home from close range at the back post.
Clyde now looked content to sit in and defend but still posed danger on the counter attack however it was Falkirk with the chances the best of which was a Telfer free kick on 75 minutes which Mitchell pushed wide.
The former Bairns keeper made one more great save on 87 minutes when Telfer's 35 yard free kick in to the box was headed on by Sammon to substitute Lee Miller at the back post.
The Falkirk player/manager didn't make the best connection but managed to send the ball goalwards and Mitchell got down low to make a fine reaction stop.
There was late hope for Falkirk on 87 minutes when a long kick by Mutch was picked up out left by substitute Louis Longridge who drove on goal and slid the ball through the legs of Mitchell from six yards to make it 3-2.
It was too little too late though and the Bully Wee hung on for the three points.