Caley cancelled out two early Dunfermline goals with two of their own in the closing 11 minutes to snatch a battling draw at East End Park.
Craig Dargo's penalty looked soft and incensed the home team and their fans, but worse was to follow with substitute Dennis Wyness equalising three minutes from the end with a stunning half volley.
There was still time for Stephen Simmons to hit the inside of the post for a seething Pars side.
Earlier home striker Noel Hunt overcame his lack of height to outjump the Inverness defence and head home a corner kick from Scott Muirhead.
Two minutes later Mark Burchill pounced on a poor headed clearance by Stuart McCaffrey before beating keeper Mark Brown with a swerving left-foot drive.
The feeling remained that two goals might not be enough for Dunfermline, but three surely would have been and Darren Young very nearly provided that extra insurance with a fierce shot which rattled the post.
Caley Thistle also struck woodwork in the 27th minute when Barry Wilson beat the wall and keeper Bryn Halliwell with his 20-yard free-kick but found the bar rather than the back of the net.
Burchill's looping header was hacked off the line early in the second half although, ironically as it turned out, it didn't seem to matter too much at the time.