The Blue Toon had to cope with injury disruption as well as full-time opposition on a difficult day at Balmoor, and had some fine goalkeeping by Brett Long to thank for their point.
Peterhead suffered an early setback as the injured Simon Ferry was replaced by recent signing Grant Savoury 17 minutes in.
Charlie Telfer then found Declan McDaid with a deft touch, but the forward’s effort was straight at Long.
Little was seen from the hosts as an attacking force as the Bairns controlled the match.
On the half hour mark Aidan Nesbitt went close from distance after his quick drive narrowly went past the post.
Falkirk looked to have broken the deadlock just before half time when McDaid found space and fired a shot towards the roof of the net, but Long made a superb save.
Jim McInally was forced into another change at the interval which saw Niah Payne replaced by Lyall Cameron.
McDaid squandered a glorious chance to put the Bairns ahead, shooting straight at Long when he found himself one-on-one.
Paul Sheerin’s side piled on the pressure and on 55 minutes Aberdeen loanee Michael Ruth had his first sight of goal when presented with the ball in the six-yard box. The striker should have scored but blazed his effort over the bar.
Falkirk were creating plenty of chances but lacking a cutting edge and Peterhead nearly took a surprise lead when defender David Wilson ventured forward and nearly caught out Paddy Martin with a long range drive.
Sheerin responded by bringing on Aidan Keena and pushing him upfront to partner Ruth and it nearly paid dividends with the Irish forward going close on 78 minutes, his effort whizzing just wide.
The Blue Toon could have snatched victory five minutes from time when Ben Hall’s slip allowed Russell McLean in, but the target man could only fire his effort straight at Martin.
Keena nearly scored a late winner when his deft header from a long ball forward caught out the Peterhead defence, but the ball flew wide.