Ten-man Livingston struggled to cling on to a match they should have had in the bag by half-time as the luckless Livvy are still seeking their first league win of the season.
Livvy started the more positive of the two sides and took the lead with the first real attack of the game. A right-wing corner from Richard Brittain was met by the onrushing Harald Pinxten, who prodded the ball home from six yards after only 14 minutes.
The Lions should have been 2-0 up 10 minutes later, but the cat-like instincts of Mark Brown in the Thistle goal thwarted the home side.
Another searching cross from Brittain was again met by Pinxten. However, the big Belgian this time elected to head the ball towards goal only for Brown to parry. Robert Snodgrass latched on to the loose ball and thought he'd put his side 2-0 up from close range, but Brown was quickly on his feet to block the youngster's effort.
Inverness rolled up their sleeves for the second half and came close with an excellent effort. Barry Wilson ghosted past two defenders but saw his shot drift inches wide of the far post.
It was Alan Morgan who stepped up to be the Inverness hero as the defender powerfully cracked a left-foot 25-yard free-kick into the bottom corner of the goal to claw them level.
Worse was to come for Livingston, who were reduced to 10 men. Graham Barrett was stretchered off with a serious knee injury after catching his studs in the turf.
Livvy had their backs to the wall and had to create a mini fort to weather the Inverness siege with the defensive partnership of Pinxten and Greg Strong performing admirably to keep the visitors at bay and secure a much-needed point for Livvy manager Paul Lambert.