Leinster continued on the winning trail at the RDS, with Isa Nacewa's 14-point haul helping them overcome a tough Edinburgh side.
Edinburgh scored tries in each half from Tim Visser and Chris Paterson, but Leinster full-back Nacewa kicked four penalties and converted Andrew Conway's first Magners League try to secure the narrow win.
Leinster were missing most of their internationals due to Ireland's training camp this week, their much-changed starting XV including half-backs Ian Madigan and Paul O'Donohoe.
Edinburgh coach Rob Moffat gave Alex Blair, the youngest of the Blair brothers, his debut at outside-half, while Argentinian lock Esteban Lozada was a late inclusion for Fraser McKenzie.
Leinster saw plenty of ball in the opening half but Edinburgh carried more of a try-scoring threat. After Nacewa had booted the hosts in front, some quick thinking from Mike Blair opened the way for Visser to strike.
Leinster lost possession at a midfield ruck and, noticing a mismatch on the left wing, scrum-half Blair dinked a kick over the top for Visser to chase.
Visser got to it ahead of the covering Richard Strauss, tapped it on and scored in the corner.
Paterson missed the conversion and Edinburgh captain Roddy Grant was punished by Nacewa for coming in at the side of a ruck, briefly restoring Leinster's lead.
Another gap appeared out wide when Edinburgh's Alex Grove broke through a gap and almost linked with Jim Thompson for a try.
The Scots had to settle for a penalty, Paterson doing the necessary after Mike Ross infringed at a scrum.
A darting run from Madigan, with Conway on his shoulder, saw Leinster click into gear. Their forwards were held up over the line, but with a penalty advantage Nacewa kicked them into a 9-8 lead at half-time.
Nacewa missed a long-range penalty just before the break, but it was his counter- attack which drove Leinster on for their only try, six minutes into the second half.
A quick lineout and series of rucks followed before ex-Edinburgh lock Nathan Hines popped the ball to the onrushing Conway who beat Alex Blair's tackle to cruise over to the left of the posts.
Nacewa's conversion was cancelled out by a penalty from Paterson but the game opened up for Leinster again when replacement prop David Young was sin-binned for hands in the ruck, just seconds after being introduced.
Replays showed the culprit was actually hooker Ross Ford, but it did not matter as Nacewa landed the penalty for a 19-11 lead and the hosts looked primed to take further advantage.
To their credit, Edinburgh's defence held firm and they even snaffled a try while Young was off.
Ford muscled past the otherwise excellent Strauss and Mike Blair's swift pass from the subsequent ruck sent Paterson cantering in under the posts.
Paterson converted his own try to make it a one-point game with a full quarter left to play.
However, Edinburgh could not get back into scoring range and their best chance was spoilt by a ruck offence from replacement Mark Robertson.