Falkirk made two changes from the defeat last weekend to Airdrieonians, with Aidan Nesbitt and Aidan Keena coming into the side for Callumn Morrison and Leon McCann.
The first real chance of the match came just after the ten minute mark with the home side going close.
Danny Denholm was just about to pull the trigger with the goal at his mercy, but Ryan Williamson’s last-ditch tackle diverted the ball out for a corner kick.
The hosts should have been in front after another two attempts at goal. Ryan Blair’s drive was well parried by Martin with the resulting corner seeing Aaron Steele head over.
East Fife were looking the more dangerous side but on 16 minutes they were reduced to ten men, with young goalkeeper Jude Smith handling outside the area and subsequently being sent off.
Kevin Smith was the player sacrificed with substitute Scott Gallagher coming on.
Falkirk began to take control of the match and Charlie Telfer sent two efforts wide from range, but outwith that the Bairns didn’t do anywhere near enough with the man advantage.
It would be the hosts who would go closest in the first half with another shot deflected wide on the counter attack just before the break.
New signing Jaze Kabia was brought on for Aidan Keena as the Bairns looked to bring more attacking threat to the second half of the match.
The Livingston loanee did just that on 53 minutes, scoring the opening goal with a glancing header after a perfect delivery from Craig McGuffie.
East Fife nearly grabbed an equaliser out of nowhere when Scott Mercer snuck in at the back post and forced Martin into a smart stop.
McGuffie should have made it two on 66 minutes when he blasted over a curling effort inside the box after Telfer found him free in the area.
Chris Higgins was lucky to escape with just a caution after a heated moment with Kabia, the defender appeared to make contact off the ball with the goalscorer, but to the amazement of the travelling support referee Barry Cook booked both players for the incident.
Martin once again made a smart save on 73 minutes to keep his side ahead. Blair’s free kick from 22 yards was heading into the far corner but the young keeper made a great diving save.
The Fifers nearly had a leveller moments from the end with Martin forced into another diving save. The hosts also had a shot cleared off the line.
However it was the Bairns who sealed the three points with Kabia scoring again. The Livi loanee finished well on the break and looks like a player who can make a big impact to this Falkirk side.
East Fife: Jude Smith, Chris Higgins, Danny Denholm, Pat Slattery, Ryan Wallace, Kevin Smith, Scott Mercer, Aaron Steele, Danny Higgins, Ryan Blair, Kyle Connell.
Subs: Scott Gallagher, Leo Watson, Ross Dunlop, Jack Healy, Liam Watt, Jamie Semple, Liam Newton.
Falkirk: Paddy Martin, Ryan Williamson, Ben Hall, Brad McKay, Aaron Taylor-Sinclair, Craig McGuffie, Gary Miller, Charlie Telfer, Aidan Nesbitt, Aidan Keena, Anton Dowds.
Subs: Robbie Mutch, Jaime Wilson, Leon McCann, Seb Ross, Cammy Williamson, Mackenzie Lemon, Jaze Kabia.