Head coach Paul Sheerin made three changes after the 3-0 defeat to Airdrieonians, with Ben Hall, Craig McGuffie and Paul Dixon all coming into the side with Mackenzie Lemon, Brad McKay and Aidan Keena all dropping to the bench.
Falkirk reverted back to the 4-3-3 formation, with a more direct style of play obvious from the off and they had all the early possesion in the match.
Peterhead suffered an early setback as the injured Simon Ferry was replaced by recent signing Grant Savoury 17 minutes in.
Charlie Telfer found himself in a more advanced role and found Declan McDaid with a deft touch, but the forwards effort was straight at goalkeeper Brett 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.
There were claims for a penalty on 41 minutes when McDaid was hauled down after being played in by Nesbitt, but referee Peter Stuart quickly waived play on.
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 6-yard box.
The striker should have scored but blazed his effort over the bar as the feeling of deja vu set in - with Falkirk creating plenty of chances but lacking a cutting edge.
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 wizzed just wide.
The returning Ben Hall nearly had a nightmare moment five minutes from time when his slip allowed 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 agonisingly flew wide.
The 0-0 draw was a first clean sheet in the league for Sheerin’s side since Saturday, August 21 when they beat Clyde 3-0 at the Falkirk Stadium.
Peterhead: Brett Long, Josh Mulligan, Flynn Duffy, David Wilson, Jason Brown, Simon Ferry, Hamish Ritchie, Scott Brown, Russell McLean, Andrew McCarthy, Niah Payne.
Subs: Lenny Wilson, Andrew McDonald, Derek Lyle, Lyall Cameron, Grant Savoury, Daniel Strachan.
Falkirk: Paddy Martin, Paul Dixon, Ben Hall, Gary Miller, Steven Hetherington, Michael Ruth, Aidan Nesbitt, Craig McGuffie, Leon McCann, Charlie Telfer, Declan McDaid.
Subs: Robbie Mutch, Ernaldo Krasniqi, Aidan Keena, Samuel Ompreon, Brad McKay, Ben Weekes, Mackenzie Lemon.
Referee: Peter Stuart.