© PA Photos
With few try-scoring opportunities for either side, it was down to the fly-halves to add to the score in the first half.
O'Gara was more clinical after the break, adding three penalties inside the opening 10 minutes of the second half to put Munster nine points ahead.
Quins struggled to get possession in the second half, but managed to force a penalty when they did get the ball, allowing Evans to cut the visitors' lead to six points.
The Irish side will play Clermont Auvergne in the semi-finals.