Ryan Flynn shot the Bairns into the lead after 19 minutes and Steven Pressley's men looked to be in control of the half until St Johnstone equalised with a Filipe Morais strike nine minutes from the break.
Saints goalkeeper Graeme Smith produced a double save from Enoch Showunmi and Brian McLean as the visitors looked the more likely to grab the winner after the interval.
In the end, it was a result which neither side would have wished, with the home side sneaking a point closer to Hearts in sixth and Falkirk only closing to within two of St Mirren in 11th.
Neither side could quite settle into a satisfactory rhythm in the early exchanges but it was Falkirk who managed to register the first shot on target after five minutes.
Skipper Darren Barr had been forced to head a dangerous Morais cross away from his own six-yard box before defender Brian McLean's speculative punt forward created the opening opportunity.
Flynn was first to react but Saints goalkeeper Graeme Smith palmed away the winger's shot after he had cut inside marker Gary Irvine.
Four minutes later, the Bairns had loud claims for a penalty turned down by referee Euan Norris when Pedro Moutinho's attempt to bundle his way past Dave Mackay appeared to be halted by the prostrate defender's arm.
Norris was again the subject of the visitors' ire moments later when he failed to play advantage in their favour as striker Enoch Showunmi bore down on goal.
In the 13th minute St Johnstone finally carved out a chance of their own. Morais did well down the right flank but on-loan Celtic striker Cillian Sheridan headed well over when he should have done better.
And six minutes later it was the Bairns who took the lead.
Smith's clearance was seized upon by Burton O'Brien and the midfielder's magnificent pass split the home defence to allow Flynn to coolly slot past the exposed Saints goalkeeper.
Falkirk always looked dangerous on the break and Jody Morris was forced into a last-ditch tackle to prevent Scott Arfield from pulling the trigger on one incisive raid forward.
However, 10 minutes from the break, Saints produced an equaliser out of nothing.
Murray Davidson produced one of his trademark bursts from midfield to cause havoc in the visitors' rearguard and Morais evaded Barr's attempted block to blast a right-foot shot into Robert Olejnik's near post.
St Johnstone began the second period on top but were again finding the Falkirk defence a tough nut to crack.
And it was Falkirk who carved out the first opportunity of the half in the 53rd minute.
Enoch Showunmi's lay-off sent Flynn scampering down the left and his eventual shot was headed just too high by the towering marksman, who had made his way into the heart of the box.
A free-kick handed the home side the chance to threaten at the other end in the 57th minute and Michael Duberry should really have done better than glance Morais' set-piece wide from barely four yards out.
The right side of the home defence again looked vulnerable in the 75th minute as Falkirk full-back Marc Twaddle got the time and space to send in a deep cross but Showunmi looped his header over from eight yards out.
Bairns substitute Carl Finnigan won the corner from which the visitors had a second penalty claim of the match turned down as Craig appeared to handle Flynn's centre.
And with seven minutes remaining Saints keeper Smith kept his side level with a double save.
Twaddle's long free-kick was headed on target by Showunmi and Smith got down to block the striker's effort and McLean's follow-up shot from a tight angle.
Craig shot wide with five minutes remaining and Arfield dragged his effort past in injury-time as both teams sought the winner but had to settle for a share of the spoils.