The home team took an early lead when Charlie Adam curled home a free-kick after Darren Dods was sent off for his challenge on Kris Boyd. As the last man Dods had to go but it still looked a harsh decision.
This draw allows Aberdeen to close the gap to five points in the race for second place and Rangers will be kicking themselves for slipping up against ten men.
The home team started well and Inverness keeper Mike Fraser did well to parry Barry Ferguson's volley after Dado Prso's cross had created the chance.
Dods appeared to pull back Boyd as the Rangers striker powered away from him and referee Willy Collum immediately red-carded the centre-back.
If this was bad, worse was to follow for Thistle as Adam bent his free-kick around the wall and into the corner of the net.
Rangers seemed to think the game was won at this stage and lost all momentum as Thistle reorganised their defence with the introduction of Stuart McCaffrey.
Fraser produced a brilliant point-blank save to deny Boyd on the hour mark before the striker shot wildly over under no real pressure.
The visitors were increasingly dangerous on the break and the warning signals were there when Russell Duncan's quickly-taken free-kick from 35 yards nearly caught out Allan McGregor, but the keeper recovered to touch the ball over.
Thistle equalised when Graham Bayne nodded down a cross at the back post to Dargo who was able to force his shot just over the line despite McGregor's best efforts.
Rangers desperately sought a winner but substitute Chris Burke's shot, which was deflected just over the bar, was the closest they came.