Falkirk started the brighter and David van Zanten had to head an Anthony Stokes cross for a corner, but Mark Corcoran responded by racing on to a Garry Brady pass only to strike his angled drive past a post.
Russell Latapy was pulling the strings for the Bairns, but Corcoran's pace was troubling the visitors and the speedy striker just failed with a flicked effort from Richard Brittain's cross.
Falkirk 's lead-up play was delightful but their lack of penetration was summed up by Stokes' weak header from Liam Craig's cross which went wide.
Stokes, though looking offside, ran on to a through ball but Chris Smith deflected the low shot for a corner.
Saints looked hungrier after the break. John Sutton, struggling to make significant impact, fired well over and Corcoran claimed a penalty when brought down by Stephen O'Donnell.
Falkirk were still building clever moves, but Saints defended efficiently and relied on Corcoran to instigate their own attacks with his pace.
From one break, Latapy chased back to prod the ball back to Scott Higgins, but referee Conroy awarded no free-kick.
A poor Lappin corner was not cleared and Kevin McGowne cut the ball back for Brady to set up Lappin, who made amends with a stunning left-footed curling shot from 25 yards which beat Higgins completely.
Stokes was not far away with a late free-kick, but Saints played to the final whistle near the Falkirk goal-line.