The Irish province had led 21-3 five minutes before the break but then came a Glasgow fight back which saw the Scots lead 24 -21 until the home side pulled away again in the closing stages.
Girvan Dempsey had collected Leinster's first try which was soon followed by a touchdown from Victor Costello, and with David Holwell converting both Leinster were 14-3 ahead after only 20 minutes. A long Holwell skip pass sent D´Arcy jinking through the Glasgow cover for his first score five minutes before the break. However Parks kicked his second and third penalties to reduce the gap somewhat at the break.
It was a different game early in the second period with first Paul Dearlove and then Sean Lamont scoring to help Glasgow level the game before Parks edged them ahead. Finally it was down to the potential Lions centre partnership to seal the game with first O'Driscoll and then D'Arcy scoring to see Leinster into the semi finals.