But the visitors' manager Gary Holt bemoaned the fact his team had failed to take the three points in more comfortable fashion after the home side had been reduced to 10 men with over an hour of the contest remaining.
"It wasn't the most enjoyable 90 minutes in my time as a manager," reflected Holt, "sometimes it's more difficult to play against 10 men and that was certainly the case today.
"We were playing a lot better when it was 11 v 11, but the sending-off changed the game. Credit to Livingston for the way they reorganised, but we were a bit sloppy and maybe some of the players thought the job had been done."
The moment which defined the game arrived after 26 minutes when Falkirk midfielder Conor McGrandles collected a pass from Phil Roberts before advancing into the Livingston penalty area, where he was sent crashing to the ground by a challenge from teenage defender Coll Donaldson.
Referee Kevin Graham had no hesitation in awarding a penalty and showing Donaldson a straight red card before Rory Loy stepped up to send the spot kick past Darren Jamieson for what proved to be the only goal of the game.
Earlier, Falkirk had been dominant with Jamieson saving well from Mark Millar and Loy squandering an excellent chance after the Livingston keeper had mishandled a pass pack from Donaldson.
But, in the aftermath of Donaldson's dismissal, Holt's men appeared surprisingly hesitant and they had goalkeeper Michael McGovern to thank for ensuring they retained their lead at the interval, the Ulsterman twice saving well from former Celtic striker Mark Burchill.
Livingston were by far the more assertive side after the interval and, although Loy did miss an opportunity to record his second goal of the afternoon when he fired over the bar with only Jamieson to beat, the better chances fell to the home side and, in a frenetic finish to the game, Marc McNulty watched in agony as his close-range, stoppage-time effort was blocked on the line by Falkirk defender Will Vaulks.
Livingston manager John McGlynn had no complaints about the red card shown to Donaldson but paid tribute to the manner in which his players had reacted following the decision.
"I felt we dominated the game after the sending off," said McGlynn, "We kept passing the ball and had a number of chances to equalise.
"I'm very proud of my players and I'm really gutted for them. It was a real injustice that we didn't take anything from the game."