Brave Borders failed by a whisker to pull off their best ever Celtic League triumph at Netherdale.
Title-chasing Leinster were red hot favourites in the wake of their stunning Heineken Cup success against holders Toulouse.
But the fired-up Reivers made them toil much more than the French giants did last weekend.
The province made a powerful start and it was no surprise when they surged ahead with a try in the ninth minute.
They secured clean lineout ball in the home 22 zone and the Reivers defence had no answer to their expertly executed pack drive which set up the score for Guy Easterby.
Borders reacted in positive fashion to repair the early damage, Calum MacRae slotting two penalties in quick succession from close range.
But his strikes simply spurred the visiting forwards into more attacking action at the other end, with prop Ronan McCormack claiming the vital touch at the end of another unstoppable rumble.
MacRae completed his penalty treble with a superb 45-metre effort — only to see former England Test front-row ace Will Green collect Leinster's third try straight from the restart.
Having missed his earlier attempts, Felipe Contepomi slotted the conversion, though MacRae hit back with another three points as the end-to-end action continued.
Contepomi replied in identical style, but the Reivers again rallied to carve out a touchdown for full-back Stuart Moffat, goaled by MacRae from the widest possible angle.
However, there was still enough time before the break for Contepomi to convert his own try to make sure of the precious bonus point for Leinster.
Borders refused to buckle and when MacRae added the extras to an opportunist score by Gregor Townsend, the match was back in the balance.
The frantic exchanges continued until the end with Contepomi adding a penalty and try for the Irish outfit and Nikki Walker going over for the Reivers.
MacRae's fifth penalty set up a tense finale but the visitors held on to win by a single point.