Leinster overcame stern resistance from Edinburgh to claim victory in the RaboDirect Pro 12.
Edinburgh's Tim Visser and Leinster's Isaac Boss exchanged tries as the visitors built up a 19-13 lead.
Visser went over again in the second half but Leo Auva'a crossed the line to turn the match in Leinster's favour.
Jonathan Sexton kicked 23 points to put the Irish province side in command and Matt Scott's try came too late for Edinburgh to turn the match around.
Victory takes Leinster to within two points of league leaders .
After some early Leinster pressure, a knock-on by Rob Kearney gave Edinburgh some territory and a further infringement allowed Greig Laidlaw to kick the hosts ahead.
Leinster went back on the attack and Kearney burst clear towards the try line only to be tackled by Visser.
In the melee that followed, Allan Jacobsen was penalised and Sexton, one of many players returning from World Cup duty, kicked the visitors level.
Edinburgh came within inches of the try line moments later in a move involving Chris Paterson, Stuart McInally and Geoff Cross but Leinster somehow scrambled the ball into touch.
From the line-out, a maul ensued and Dave Denton attempted to squeeze the ball over but, after consultation with the TMO, the referee awarded Leinster a scrum, from which they cleared.
There was more frustration for Edinburgh moments later as Steven Turnbull broke through but did not release in time and Leinster's next break produced a penalty, from which Sexton was again successful.
But the Scottish side regained the lead when Visser weaved his way through the Leinster defence off Laidlaw's neat pass and touched down, giving captain Laidlaw a simple conversion.
Sexton replied with a penalty and Boss then got Leinster's first try after wrongfooting Edinburgh with a clever dummy and going over to touch down between the posts. Sexton converted.
Laidlaw and Sexton exchanged penalties to establish a six-point gap at the turnaround, Visser unable to retrieve Nick de Luca's looping pass in Edinburgh's last serious attack of the first half.
The second period was just getting warmed up when Visser received Paterson's pass and sped down the left, beating three tackles in the process, and slid in under the posts, Laidlaw converting.
Sexton kicked Leinster back in front but Laidlaw soon reversed that.
Auva'a touched down in the corner off Kearney's offload but Sexton missed the conversion and his next penalty attempt.
However, Sexton's next penalty and a drop-goal from the fly-half stretched Leinster's lead to 10.
Laidlaw missed his next penalty but Harry Leonard's superb kick through released Scott for his try.
Another miss by Laidlaw meant Edinburgh faced a five-point deficit in the closing stages.
And Edinburgh's hopes of a bonus point were dashed by a further Leinster penalty, this time by Fergus McFadden, in the closing seconds.
Edinburgh: Paterson, Webster, De Luca, Scott, Visser, Leonard, Laidlaw, Jacobsen, Ford, Cross, Lozada, S. Turnbull, Denton, Grant, McInally.
Replacements: Thompson for Paterson (70), T. Brown for Webster (63), Lawrie for Ford (71), Niven for Cross (73), Gilchrist for S. Turnbull (63), Talei for McInally (63). Not Used: Traynor, M. Blair.
Leinster: R. Kearney, D. Kearney, O'Malley, McFadden, Fitzgerald, J. Sexton, Boss, van der Merwe, Cronin, Ross, Cullen, Toner, McLaughlin, Ryan, Auva'a.
Replacements: Madigan for J. Sexton (80), Strauss for Cronin (50), R. Ruddock for McLaughlin (57). Not Used: McGrath, White, Sykes, Cooney, Carr.
Ref: Leighton Hodges (RFU)