Genuine chances were rare but the first fell to the visitors. Andrew Nelson broke down the channel and his beautifully floated cross just evaded Thomas Robson.
Falkirk were dominating possession and Alex Jakubiak brilliantly controlled a fizzed cross before firing a left-footed half-volley that Neil Alexander tipped over.
Livingston squandered a brilliant opportunity to open the scoring on 25 minutes but Scott Pitman headed over a Jackson Longridge cross from only six yards.
As the game entered the final quarter, Ryan Hardie ignored the run of Pitman and fired straight at Connor Hazard before glancing a header narrowly wide minutes later.
With the game trudging towards a stalemate, Livingston substitute Lee Miller almost won it against his former side. The veteran striker peeled off his marker to head a Rafa De-Vita cross goalwards but Aaron Muirhead brilliantly cleared.