Ten-man Inverness held out for a share of the points against Clyde thanks to an impressive defensive effort in the second half.
But it was a moment of madness from striker Martin Bavidge just a minute from the interval that left them in trouble.
Bavidge needlessly hauled down Darren Murray as the Clyde player skipped past him and was promptly red-carded.
Until then Inverness had been on top and deservedly opened the scoring in the sixth minute when Bavidge picked out Dennis Wyness with his cross, and the striker sent his low shot beyond keeper Bryn Halliwell.
However, as Clyde battled back Inverness keeper Jim Calder twice denied Jamie Mitchell as he turning both his shots over the bar.
But he had no answer on 73 minutes when Mitchell met a corner and sent a looping header into the corner of the net.