Despite considerable pressure, especially in the first half, Steven Pressley's bottom-placed side were unable to conjure a goal at the Falkirk Stadium.
With rivals Killie winning at Aberdeen, the Bairns fell two points adrift and must now emulate last season's final-day victory at Inverness to avoid dropping to the First Division for the first time since 2005.
St Johnstone, who extended their unbeaten run to five matches, had a strong penalty claim in the second period when substitute Josh Falkingham appeared to be brought down by goalkeeper Robert Olejnik.
But they were left happier with the draw as they stayed a point ahead of Hamilton in the race for seventh place.
Pressley made one change from the team that drew at home to St Mirren with Enoch Showunmi restored for Mark Stewart.
St Johnstone brought in Steven Anderson and Cillian Sheridan for Kevin Rutkiewicz and Liam Craig following Saturday's 2-1 win at Kilmarnock.
Despite the Bairns' greater cause, the attacking 4-3-3 line-up from Perth boss Derek McInnes proved his desire for the points.
Jody Morris registered an early, weak effort wide, but Falkirk took control to dominant the first half.
Pressley's energetic charges were almost rewarded on seven minutes when a corner from the right was headed on by Showunmi only for Pedro Moutinho to blast a glorious chance over from close range.
Falkirk continued to show a real appetite for the contest but opportunities proved hard to come by.
Scott Arfield's one-two with Moutinho on 16 minutes threatened success but the former could only drag a low shot into Graeme Smith's grasp.
The Bairns continued to hold the ascendancy but after promising build-up play, their final ball let them down.
Saints striker Kenny Deuchar, a former Falkirk player, was cautioned on 26 minutes for dissent before the injured Murray Davidson trooped off to hand ex-Leeds youth Falkingham a midfield debut.
Morris was next to be yellow-carded by referee Craig Thomson after a foul on Marc Twaddle.
As Falkirk upped the pressure, their best chance soon came. Moutinho's corner picked out Tam Scobbie who stretched to head just a yard wide of the left upright.
On 38 minutes, Colin Healy's short corner then caught the visiting rearguard napping and Moutinho's 15-yard strike was only denied by the legs of Smith. The Portuguese striker soon flashed a long-range free-kick past.
Saints defender Steven Anderson lost his footing and hauled down the on-rushing Showunmi, becoming the third Perth player booked shortly before the interval.
McInnes made a second change at the break, Sheridan replaced by Paul Sheerin.
The McDiarmid Park side began the new half brighter, at least territorially, and they finally carved out a chance on 52 minutes.
After Morris was felled by Twaddle, Danny Grainger's free-kick picked out Deuchar who nodded just over.
Falkirk, with just one goal in their previous three games, were struggling to regain the initiative despite the backing of almost 5,000 home fans.
Saints substitute Sheerin had a clear sight of the net after Chris Millar flicked the ball into his path but the veteran midfielder blazed wildly past left-footed.
St Johnstone had a new solidity and Falkirk were struggling to fashion any kind of opening.
However, on 68 minutes, they almost profited on the break. Moutinho played in Showunmi who steadied himself before seeing his shot deflected into the path of Ryan Flynn who nodded inches wide.
Falkirk then appeared to have a penalty let-off at the other end. Olejnik looked to rush out and fell Falkingham but whistler Thomson, despite a furious protest from the Saints player, was unmoved.
McInnes also showed his displeasure to the fourth official Gary Hilland on the touchline.
At the other end, Flynn was made to rue a poor first touch as he bore down on goal.
Falkirk pushed for the winner in a frantic finale, with Arfield somehow denied by Smith's tip past the far post, but a much-needed goal fail to come.