And in the end it was Ulster's indiscipline which cost them dear, Jonathan Sexton on target with two penalties, a conversion and a drop goal, while Ruan Pienaar struggled from the kicking tee.
Kevin McLaughlin's scored the only try for Leinster early on while Johann Muller scored his first try for Ulster.
But it was Pienaar's goalkicking struggles which held back the home side and they now require a miracle in order to make the play-offs with the Heineken Cup now taking priority ahead of a semi-final against Edinburgh next weekend.
Leinster had the better of the early stages and took the lead after just seven minutes when the Ulster defence left a huge gap for McLaughlin to run straight through and over the line.
However despite dominating early on, Leinster struggled to add to that lead and with 25 minutes gone, Ulster got themselves on the scoresheet.
Paddy Wallace produced the spark that turned an attack which looked to be going nowhere into a tryscoring opportunity.
And with an overlap created it was skipper Muller's first try for his province which got Ulster back to within two points, Pienaar missing his second kick of the night after an earlier penalty against the post.
The same could not be said of Sexton who stretched the visitors' lead to five with a penalty just before the half-hour.
But despite the home side spending most of the half under the cosh, Ulster won themselves another penalty two minutes from half-time and Pienaar finally found his range to make it 10-8.
Ulster could not hang on to that score before half-time though, Willie Faloon giving away a penalty in front of the posts to allow Sexton to make it 13-8 at the break.
The home side made the better start to the second half but Pienaar missed his third kick of the night as Leinster maintained their lead.
A scrappy period followed with neither side able to break through some impressive defence, but it was Leinster who secured the next points.
A few charges from the visiting pack looked like setting up a try however Ulster kept them out and Sexton instead chose to slot an easy drop goal.
In a disappointing end neither side was able to create any more and Leinster comfortably held on for the win.
|Ulster Rugby Score Card|
|Leinster Rugby Score Card|