Higdon, who rescued the Bairns from relegation last season, scored one of the best goals of the current campaign when he volleyed home from 35 yards.
But Finnigan had the final say with a dramatic equaliser two minutes from time to prevent rock-bottom Falkirk falling five points adrift at the foot of the table.
Toufik Zerara made his Falkirk debut as both sides made two changes for today's game, Marc Twaddle also coming in for the visitors.
St Mirren recalled captain John Potter and midfielder Stephen O'Donnell.
Falkirk were forced into a late change on the bench after Alex MacDonald was injured in the warm-up, the forward replaced by under-19 player Blair Alston.
Saints had not tasted victory in the SPL since their trip to the Falkirk Stadium two months earlier, while the rock-bottom Bairns had only won once all season in the league.
The hosts began the brighter but were almost caught out in the third minute by Scott Arfield's 18-yard snapshot, which was straight at Paul Gallacher.
Falkirk briefly took control before Higdon turned his marker in the 20th minute and fired a low left-foot shot which Robert Olejnik tipped round the post.
The goalkeeper then saved with his legs from O'Donnell, who was left with a tight angle after tricking his way into the area.
St Mirren were failing to make the most of a number of corners in a game of precious few openings.
At the other end, Zerara showed a brief flash of quality on his debut, pulling down a cross with ease and scuffing his left-foot finish too close to Gallacher.
The new man then teed up Vitor Lima for a screamer that deflected narrowly wide before showing Saints the way from the resulting corner, Finnigan heading his centre straight at Gallacher.
The first flashpoint of an otherwise tame game arrived two minutes before the break when Potter fell on top of Finnigan, sparking angry exchanges between both sets of players.
Falkirk were in control of proceedings after the break but were left reeling in the 53rd minute when Higdon netted a wonder goal.
The ball sat up perfectly for the former Bairns striker 35 yards out and he could hardly have connected better, his dipping volley touched onto the underside of crossbar by Olejnik but carrying far too much power to keep out.
Higdon's strike partner Billy Mehmet nearly got on the end of an O'Donnell cross moments later.
Falkirk were huffing and puffing but their lack of cutting edge was summed up when Arfield fell over sending another 18 yarder wide.
Potter somehow escaped a booking for tripping Ryan Flynn in full flight before Saints brought on Lee Mair for Jack Ross, switching around their full-backs.
Higdon had the ball in the net again in the 70th minute but referee Craig Thomson spotted an infringement.
Falkirk then withdrew Flynn for Lee Bullen and Arfield for Danijel Marceta.
A moment of real controversy arrived 13 minutes from time.
Pedro Moutinho sneaked up behind Gallacher as the keeper was bouncing the ball, robbed him and steered it into the net.
However, Thomson chalked off the goal, much to the fury of the Falkirk players and fans.
Finnigan was then off target with a diving header from Marceta's cross before Saint Mirren brought on Steven Robb for O'Donnell.
With time running out, Bullen headed a corner over the bar before being denied by a Potter block after Gallacher had come rushing out of his goal.
But Falkirk finally got the breakthrough in the 88th minute when Moutinho beat three men and slipped in Finnigan, who kept his cool to fire low across Gallacher.