After Marc McAusland had given the hosts an early lead, Josh Meekings grabbed a second half equaliser for the Scottish Premiership high-flyers who will go into the forthcoming replay at the Caledonian Stadium as the clear favourites to reach the last 16.
Following an undistinguished opening quarter of an hour to the game, Saints took the lead through McAusland who latched on to Jason Naismith’s cross to sidefoot home from close range.
And the hosts almost added a second via Kenny McLean whose volley flew wide on 28 in front of less than two thousand spectators.
Although the visitors dominated possession, they were unable to grab an equaliser before the break with Ross Draper, David Raven and Billy McKay all off target at Greenhill Road.
Early in the second half, St Mirren had another opportunity to extend their lead when Naismith set up Steven Thompson who skied his effort over the bar.
However, Inverness were deservedly level on 63 when the hosts failed to clear a corner, Gary Warren struck a post and Meekings crashed home the rebound.
During the remainder of this fiercely contested cup tie, it was Inverness who came closest to grabbing a winner with Ryan Christie firing narrowly wide from outside the box with 90 minutes on the clock.