Bairns substitute Carl Finnigan cancelled out Collin Samuel's second-minute opener only three minutes after the break but the three points stayed at McDiarmid Park for the first time since Saints were promoted in the summer.
Home substitute Chris Millar regained his team the lead in the 64th minute and only two minutes later Murray Davidson made sure of the win following a mistake from Falkirk keeper Robert Olejnik.
It was another body blow for bottom side Falkirk and under-pressure boss Eddie May, whose managerial career has got off to the worst possible start since succeeding John Hughes in the summer.
St Johnstone could not have wished for a better opening to the match as they took the lead after only one minute and 23 seconds.
Dave Mackay's cross was not the best from the right flank but when Brian McLean misjudged the flight of the ball as he attempted to chest it away he only succeeded in setting up Samuel.
Saints' top scorer was never going to miss from 10 yards out and he rippled the net for his sixth of the season.
To make matters worse, experienced full-back Jackie McNamara was injured in the build-up and had to make way for the fit-again Finnigan in a reshuffle that at least paid dividends for the visitors after the break when the striker scored.
The Bairns responded well to conceding such an early goal but the Perth men should have been two ahead in the 15th minute.
Kenny Deuchar sent Samuel into the right-hand channel but when his cross perfectly picked out Liam Craig the midfielder somehow missed the open goal.
Davidson's chance two minutes later was harder but he would still have been disappointed not to have got his header on target from Craig's curling cross.
Jody Morris came close in the 26th minute with a shot on the drop that whistled past the top corner of Olejnik's goal and although Falkirk pressed for the equaliser with the benefit of plenty of possession they lacked a cutting edge.
St Johnstone had enjoyed the perfect opening to the first half but it was Falkirk who came flying out of the traps following the break and finally found the incisiveness to grab the equaliser after only three minutes.
Marc Twaddle's ball forward was flicked on brilliantly by Kjartan Finnbogason for strike partner Finnigan and the former Newcastle youngster rattled his volley past the exposed Smith from just inside the box.
The strike stunned the home side but half-time substitute Millar sent Saints back in front in the 64th minute.
An untidy attack climaxed with the ball falling for Millar on the right side of the area and his shot across Olejnik beat the keeper's despairing dive.
And within two minutes, the McDiarmid Park outfit effectively sealed the win with a third that was all down to Olejnik's error.
Craig sent in a deep free-kick from the right and when Olejnik came and failed to gather the set piece Davidson headed in the ricochet from close range.
Falkirk had appeals for a penalty brushed aside by referee Dougie McDonald in the 71st minute when Graham Gartland bundled into the back of Finnbogason as the former Celtic youngster attempted to latch on to Mark Stewart's cutback.
However, Saints' quick-fire double had knocked the stuffing out of the Bairns and it was the home side who finished the game on top and seeking a fourth goal.