Tete Yengi's first-half strike drew Livingston to within three points of Scottish Championship leaders Falkirk.
After a scrappy opening 40 minutes, Livingston took the lead when the towering Yengi sized up a shot from outside the box and beat Nicky Hogarth emphatically.
Hogarth then denied Stephen Kelly shortly before the break.
Falkirk were foiled and frustrated by Livi in the second half as they lost for the second time in the league this season.
Ayr United also moved closer to the leaders, with Scott Brown's side seven points off Falkirk and four behind Livingston.