A late Sonny Parker try ensured the Ospreys maintained their 100% record in a tense, table-topping clash.
The home side dominated territory at St Helen's, but with 10 minutes left good Irish defence and Gavin Henson's missed kicks meant they led by just 6-3.
David Holwell, who scored Leinster's only points, was then sin-binned for killing the ball on the ground.
The Ospreys took advantage, Adrian Durston breaking the line with a side-step before Parker scored out wide.
The home side enjoyed a monopoly of the early territory and possession, but a superbly disciplined Leinster defence held them
comfortably at bay.
Malcolm O'Kelly finally snapped in the 17th minute, conceding a penalty which allowed Henson to open the scoring.
But the Irish side's bruising, experienced pack was starting to get the better of the forward exchanges, and they went close
to the opening try when home full-back Durston fumbled a high kick.
The Ospreys weathered the storm, and a second Henson penalty doubled their lead before the break.
A Holwell penalty got Leinster on the scorecard early in the second period, before the Irish rolled out their big guns,
Shane Horgan and Gordon D'Arcy coming off the bench.
But the Ospreys encamped deep in the Leinster half, only to repeatedly flounder on the solid blue wall of defence, handling
errors costing the home side dear.
Henson missed two straightforward penalties against one from Holwell as the game remained on a knife-edge.
Then, with 10 minutes remaining, Holwell killed the ball on the floor. Henson missed the kick, but his opposite number
received a yellow card.
Duncan Jones rumbled off the back of the line-out against the 14-man visitors, the forwards laying back good ball.
Durston hit the line with two devastating side-steps before being brought down, but the ball was quickly spun right for
Parker to claim the decisive score.
Henson missed the conversion and a late penalty to make his tally just two out of eight.
"It was a huge challenge, an intense game against a very strong pack where no quarter was asked or given," said Ospreys coach Lyn Jones.
"That was exactly the sort of win we wanted and we deserved it, they didn't look like scoring a try despite all the quality in their backs.
"Two years ago not one Welsh side would have beaten that Leinster team, but now we've got the back-up that the Irish regional sides have had for years and we are starting to outstrip them."
Ospreys: A Durston; R Mustoe, D Bishop, S Parker, S Williams; G Henson, J Spice; D Jones, B Williams (capt), A Jones, L Bateman, B Cockbain, A Lloyd, R Pugh, R Jones.
Replacements: M Davies, A Millward, P James, A Newman, J Bater, M Jones, E Seveali'i.
Leinster: G Dempsey; G Brown, B O'Driscoll, F Contepomi, D Hickie; D Holwell, G Easterby; R Corrigan (capt), S Byrne, R Nebbett, M O'Kelly, B Gissing, A McCullen, S Jennings, D Dillon.
Replacements: E Byrne, G Hickie, L Cullen, C Potts, B O'Meara, G D'Arcy, S Horgan.
Referee: Rob Dickson (Scotland)