The visitors took a third-minute lead through Jason Naismith, but goals by Ross Draper in the 16th minute and Greg Tansey 19 minutes later turned the match in the favour of Inverness before the interval.
After the break, Sean Kelly brought St Mirren level just past the hour mark and the Buddies looked to have been handed the initiative when Josh Meekings saw red with 23 minutes still remaining - but the hosts held on.
Inverness made two changes to the line-up that started Wednesday's 2-1 defeat to Dundee United at Tannadice with Liam Polworth and Ryan Christie - both products the club's youth set-up - given starts.
St Mirren, showing four alterations from the side that lost 1-0 at home to St Johnstone, got off to the best start possible when a free-kick from Kenny McLean found its way through to the unmarked Naismith and the full-back showed great composure to take a touch before drilling the ball across goal and into the far corner.
Thistle attempted to recover from this early setback and Christopher Dilo was required to get his fingertips to Meekings' header after he had flicked on Polworth's free-kick.
The Buddies goalkeeper, however, could do nothing in the 16th minute as Inverness restored parity.
Graeme Shinnie's corner went all the way to the back post to where Draper was lurking and he rose above Darren McGregor to head home from close range.
The hosts could have been ahead moments later. Tansey's flick-on sent Billy McKay clear, but as the striker went to pull the trigger, the ball took a horrendous bobble, meaning the effort was skewed well wide of goal.
Inverness were beginning to gain control of proceedings and a Polworth free-kick from 22 yards was well held by Dilo.
St Mirren were wilting under the mid-afternoon sun and they found themselves trailing with 35 minutes gone.
Polworth's cross from the was met by McKay and he cushioned a header back into the path of the unmarked Tansey, who from 10 yards had the simplest of finishes beyond the exposed Dilo.
Despite falling out of the game, St Mirren came close to levelling matters as the interval approached, but a combination of David Raven and Gary Warren blocked away Steven Thompson's goalbound effort.
Both sides were forced into changes early in the second half, Marc McAusland replacing John McGinn for the hosts, while Nick Ross came on for the injured Tansey.
St Mirren were beginning to work their way back into the contest and after Adam Campbell's weak effort was saved, the Paisley club levelled in the 61st minute.
McLean's corner caused problems for the home defence and after Thompson had his shot blocked, the ball eventually fell to Kelly at the back post and he sent a close range header into the roof of the net.
It soon got worse for Caley Thistle midway through the second half. Josh Magennis had the pace to get clear of Meekings, who fouled the on-loan Aberdeen forward as he threatened to run in on goal, resulting in referee William Collum showing the central defender a straight red card.
Despite being a man down, Inverness almost regained the initiative, but Ross could not quite turn home a Polworth shot after good work by substitute Marley Watkins.
As the match entered the final 10 minutes, only a timely block by Raven denied McLean after Gary Teale had tricked his way past several Caley Thistle players.
However, St Mirren could not make their numerical advantage count as the points were shared.