Victor Costello captained Leinster for the first time in his nine-year career but not even the mercurial number eight could prevent the reverse.
Both sides started off edgily with mistakes coming from either side Leinster's full-back Felipe Contepomi was tackled by Scott MacLeod while trying to run the ball out of danger and was penalised for holding on. Charlie Hore took the simple pot at goal and the Borders took the lead.
The Scots' lead lasted only a matter of seconds, however, before David Holwell stroked a confident equaliser following obstruction at the restart.
It was the same story midway through the half when Hore regained the lead for Borders only to see his the scores levelled again through Holwell.
Borders replied in positive fashion, with wing Simon Danielli embarking on a 30-metre gallop before being blocked by Contepomi. However, the breakthrough try finally came in stoppage time before the break. Chris Cusiter made the initial break before John Dalziel connected with flanker Andy Miller, who crashed down over the line. Hore converted from a tricky angle to give Borders a 13-6 interval lead.
Borders kept up the momentum and should have scored again after more great work by Cusiter but captain Paul Thomson lost the ball as he dived over.
Hore added his third penalty to ease the frustrations and to increase the gap to 10 points and then scored another three points from close in. Holwell clawed back a penalty at the other end, but two minutes later Hore darted in for the second Borders try and added the touchline conversion to effectively seal Leinster's fate. UCD scrum-half Brian O'Riordan on as a late replacement reacted quickest as the ball squirted free from a 5-metre Borders scrum to bag a 72nd-minute try. However, Ally Warnock's late drop goal staved off any hopes Leinster had of a bonus point.
Despite the manner of the loss, there was some compensation for Declan Kidney, with Clontarf's Dave McAllister making his first start at centre, flanker Niall Ronan of Lansdowne continuing his fine development and former U21 David Gannon getting on for his debut in the closing stages.
34-year-old Costello said: "it was a very disappointing night at the office for us. We've got to try and lick our wounds now, and try and get something positive out of it, and move forward."
BORDERS: Moffat, Walker, MacRae, Hore, Danielli, Warnock, Cusiter, Thomson, Ford, Douglas, MacLeod, Stewart, Dalziel, Gray, Millar.
LEINSTER: Contepomi, Norton, Lewis, McAllister, Brown, Holwell, O'Meara; Lyne, D. Blaney, Nebbett, Potts, Gissing, McCullen, Costello, Ronan.
Replacements: David Quinlan for Lewis (18 mins), Gavin Hickie for Blaney (35-40 mins, 73-ft), Brian O'Riordan for O'Meara (50), John McWeeney for Norton (62), Peter Coyle for Lyne (73), David Gannon for Potts (80)
Referee: Neil Ballard (WRFU)