Munster were staring at a 23-6 scoreline early in the second half, but clawed their way to within the crucial seven-point margin through the boot of O'Gara and a try for centre Lifemi Mafi.
Their cause was helped immeasurably by English referee Rob Debney showing yellow cards to Clermont trio Loic Jacquet, Julien Malzieu and Alexandre Audebert.
Fly-half O'Gara, who kicked 14 points, said: "I have to say I didn't realise the bonus point was still in play at the end - it was all a bit crazy.
"People don't realise how tough Clermont are. They're a fantastic side and that was a really tough game.
"We came here looking for the win, and we're disappointed not to have it, but we got the bonus point and that's enough to take into our next game into Wasps."