Michael O’Halloran and Steven MacLean came closest to scoring for the home side in the first half but both were denied in quick succession.
Kilmarnock almost won it 10 minutes from time but Nathan Eccleston’s shot was heroically blocked by Tam Scobbie in the midst of a dramatic goalmouth scramble.
Clear opportunities were few and far between for much of the match, and the sides remained seventh and eighth respectively in the table.
Ecclestone had the first attempt of the match but Alan Mannus was able to gather at the second attempt, while at the other end Chris Johnston’s 20-yard left-footed shot was just inches wide of upright.
Those chances spurred the hosts into action and it looked like the opening goal was set to arrive when O’Halloran was denied at close range by Craig Samson and MacLean followed up with the rebound, but the striker’s goal-bound effort was blocked by Darryl Westlake.
Chris Kane shot straight at Samson on the turn and David Wotherspoon also forced the away goalkeeper into action when his effort was saved after a purposeful solo run into the penalty area.
St Johnstone were enjoying more of the possession and territory, but Kilmarnock threatened as the first half drew to a close when Tope Obadeyi’s powerful effort had to be parried to safety by a diving Mannus.
Gary Locke’s side threatened after the break when Johnston set up Eccleston, but the striker could not get enough purchase on his effort to trouble Mannus.
O’Halloran had struggled to make his usual impact in St Johnstone’s attacking play but he did create an opening midway through the second half when he cut inside from the left and lashed an effort towards the far corner that a diving Samson pushed to safety.
Kilmarnock responded when Murray Davidson was dispossessed by O’Hara and the midfielder played in Eccleston. The forward weaved his way past two defenders in the penalty area, but Mannus was equal to his attempt.
Davidson hooked an effort straight at Samson after Wotherspoon’s chip into the box had caused chaos in the away defence, but both sides were struggling to find enough space to produce a meaningful shot on goal.
A moment of madness almost gifted Kilmarnock a winner with 10 minutes to play.
Steven Anderson inexplicably lost possession to Johnston, who raced in on goal and forced Mannus to save with his feet.
Eccleston was perfectly placed to score from the rebound, but substitute Scobbie somehow threw his body in his way to block, by which point Mannus was back on his feet to tip away another follow-up effort from Josh Magennis as St Johnstone somehow escaped.
As the clock wound down, the hosts won a succession of late corners and crosses as well as forcing Samson to save from Danny Swanson, but they were unable to find a breakthrough.