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The away side needed just two tries either side of half time against a much improved Connacht to claim the points.
Leinster, despite conceding an early 9-3 lead, defended well to limit their opponents to two David Slemen penalties and a drop goal, all socred in the first 20 minutes.
The game was ended as a contest thanks to an onslaught by Leinster both before and after the half time break.
Jamie Heaslip had a searing 60 metres break from Shane Horgan to thank for his score moments before half time and, just seven minutes after the restart, Girvan Dempsey was on the end of a flowing move to go in at the corner.
Felipe Contemponi converted one try and landed two penalties to complete the scoring and a miserable day for Connacht who could not force their way over the line despite camping out on the Leinster line late in the game.