Sportal.co.nz 08.Apr.2013Getty Images
Six penalty goals to the Ireland international were enough for Munster, while Nick Evans booted all 12 of Quins' points at The Stoop.
Munster will meet ASM Clermont Auvergne at the Stade de la Mosson in the final four on April 27, after eliminating the previously unbeaten Harlequins.
Evans' kicking had Quins ahead 9-6 at the interval, but a 15-minute purple patch from the Munster forwards gave O'Gara four chances at points - and he converted the lot to put his side on top.
On a day for kickers, England's Jonny Wilkinson scored all of Toulon's points in their 21-15 victory over Leicester Tigers at the Stade Felix Mayol.
Wilkinson kicked six penalty goals, and also added a dropped goal in the last minute to boot his side to victory.
Wilkinson's fellow Englishman Toby Flood scored all 15 of the Tigers' points from penalty goals, firing them 9-0 ahead inside 20 minutes.
After two Wilkinson replies, Flood could have made it a six-point buffer at the interval but skewed his attempt.
And two more penalties to Toulon early in the second half, converted by Wilkinson, gave the French club the upper hand - one they wouldn't rescind.
Toulon will meet Saracens at Twickenham on April 28 for the chance to play off in the Cup final at Aviva Stadium on May 18.