The visitors led at half-time courtesy of Dave Mackay's first goal for the club and St Mirren initially struggled to get back in the game.
But a double substitution sparked more life into the hosts and one of the introductions, on-loan Celtic player Graham Carey, set up the 71st-minute equaliser with a curling free-kick into the box.
Both sides went all out for victory in an entertaining finale that was in stark contrast to the opening quarter, when neither side could capitalise on periods of possession.
St Mirren manager Gus MacPherson continued with the three-man central defence that secured cup success against Hearts and Rangers, who were held to a Scottish Cup draw in Paisley on Saturday, and his team showed good spirit to avoid their fifth consecutive SPL defeat.
Both defences were on top at the start, although there was a brief moment of concern in the visiting box when Graeme Smith initially failed to read Michael Duberry's decision to leave a bouncing ball, but the goalkeeper recovered.
Liam Craig forced the first save with a 25-yard strike which Paul Gallacher pushed over, but the visitors scored from the resulting 33rd-minute corner.
Jack Ross cleared Peter MacDonald's hooked effort off the line after Duberry had headed the ball down, but Mackay rattled home the rebound from eight yards.
The Perth side chased a second and Gallacher held MacDonald's header from a Danny Grainger cross. The St Mirren goalkeeper was soon beaten to a Filipe Morais cross by Steven Milne but the striker's close-range header bounced off the crossbar.
St Mirren pressed in the opening stages of the second half but made little headway and Mackay came close to his second when his header drifted just wide from Craig's cross.
Billy Mehmet's strength against Duberry set up a half-chance for Higdon, but the former Falkirk man's 20-yard effort was weak and straight at Smith.
The double switch came on the hour mark with Craig Dargo coming on for Stephen O'Donnell and debutant Carey replacing David Barron at wing-back, with Mehmet dropping into midfield.
St Johnstone threatened on the break with Milne slicing wide after latching on to MacDonald's flick-on before the St Mirren substitutes combined to create a great chance.
Higdon laid the ball off after Dargo had helped on Carey's cross but Andy Dorman shot wide from 10 yards.
Mehmet saw a shot on the run deflect wide before St Mirren's pressure paid when Higdon guided Carey's left-wing delivery into the corner of the net.
Morais was replaced by Paul Sheerin, whose first touch was a first-time volley that had Gallacher scrambling to hold. Another Perth substitute, Cillian Sheridan, had a shooting chance after good work from Jody Morris but he scuffed his effort from 25 yards.
In an open finale, Dorman headed across the face of goal from Ross's cross and MacDonald and Morris both just failed to convert in the six-yard box for the visitors.