In a match featuring 10 tries, scores from Jordan Larmour, Jamison Gibson-Park and Jack Conan in the space of 10 minutes in the third quarter proved crucial, taking the visitors from 19-12 behind to 33-19 in front, and they did just enough to close out the win.
Edinburgh handed competitive debuts to Paul Hill, Ross Thompson and Mosese Tuipulotu, while Scotland wing Darcy Graham was back after eight months out due to injury.
Leinster arrived in the Scottish capital without several of their Ireland internationals, including Caelan Doris, Josh Van Der Flier and Robbie Henshaw, but were still able to send out a strong and experienced side.
After weathering some early pressure from the visitors, Edinburgh thought they had gone ahead in the 10th minute when Matt Currie darted over but it was ruled out for a forward pass by Thompson. The hosts had a penalty advantage to fall back on, however, and following the resulting tap, Pierre Schoeman pushed his way over. Thompson converted.
Leinster hit back in the 16th minute when Tommy O’Brien finished off on the left after the ball was worked clinically through hands. Sam Prendergast was off target with his conversion attempt.
The visitors went ahead 10 minutes later when Charlie Tector seized on a weak box-kick from Ali Price and then skipped past the scrum-half. Prendergast converted.
Edinburgh responded in the 32nd minute as Duhan Van Der Merwe ran in on the left following some brilliant build-up play from Thompson and Jamie Ritchie. Thompson missed the conversion, and the match was deadlocked at 12-12 at the break.
Edinburgh edged back in front in the 43rd minute when Dave Cherry scored off the back of a rolling maul, with Thompson converting.
But their lead was again short-lived as Larmour zipped over the whitewash following a lay-off from Prendergast, who again converted.
Leinster, having got themselves level again, swiftly turned the screw with further tries from Gibson-Park and Conan in the 53rd and 57th minutes, taking them 33-19 ahead.
Van Der Merwe reduced the deficit with his second of the night in the 66th minute but Ben Healy’s missed conversion meant the visitors still had some breathing space going into the closing stages.
It was just as well for the Irish as they had Ross Byrne sin-binned before Matt Scott scored for Edinburgh in the last action of the match, with Healy converting, as they secured a losing bonus point.
