The Ospreys succumbed to a Leinster side who made it 12 wins from 12 in the PRO14 as scrum woes undermined their efforts in Neath.
The Welsh region were looking to build on last week's surprise victory over Ulster that sparked hopes their season might be about to get back on track after a torrid campaign that's left them rooted to the bottom of Conference A.
And it all started well enough, with the Ospreys looking competitive in the initial exchanges at the Gnoll.
The home side dominated territory in the opening quarter, with young centre Kieran Williams impressing with his defence-busting running.
But they were frustratingly outgunned at the breakdown on more than one occasion, with Nicky Smith and Simon Gardiner also in bother at the scrum, as chances went begging.
And, after 18 minutes of relative Ospreys dominance, the unbeaten Irish side crossed for a try through replacement Tommy O'Brien following a simple move down the short side that saw the Ospreys caught napping.
Credit to the Welsh team though, they were not for folding here. Price missed a shot at goal before finally getting on the board with his third attempt as the interval approached.
And there was better to come in the dying moments of the first half when James Lowe dropped a pass and fumbled it into the grasp of the grateful Luke Morgan who galloped 60 metres to score between the posts and give the Ospreys a remarkable 10-7 lead as Price added the inevitable extras.
The unexpected advantage wasn't to last long after the break as flanker Josh Murphy eventually claimed the next score, barreling over from close range after Leinster had been camped on the hosts' try line for several minutes of dominant scrums that saw the Ospreys pack warned about the impending threat of a penalty try as they struggled to survive at the set-piece.
Those issues saw prop Simon Gardiner and hooker Scott Otten replaced by Gheorghe Gajion and Sam Parry before the midway point of the second half.
And their troubles were compounded when Williams, who was superb for a second consecutive week, was forced to leave the field before the crucial final quarter after being caught in the face by the stray boot of team-mate Sam Cross.
The Ospreys continued to hang in though, winning a couple of key turnover penalties as Price narrowed the gap to a single point following a Leinster infringement on the ground.
But they were battling against the tide and were reduced to 14 men for the final eight minutes after Parry took the fall for one too many Ospreys indiscretions.
Soon after Cian Kelleher scampered home in the corner to secure the win, with replacement Harry Byrne's difficult conversion denying the home team a losing bonus point.
Tries: Luke Morgan
Cons: Luke Price
Pens: Price (2)
Tries: Tommy O'Brien, Josh Murphy, Cian Kelleher
Cons: Ciaran Frawley (2), Harry Byrne (1)
Ospreys: C. Evans; H. Dirksen, O. Watkin, K. Williams, L. Morgan; L. Price, A. Davies; N. Smith, S. Otten, S. Gardiner, A. Beard, B. Davies, D. Lydiate, O. Cracknell, D. Baker.
Replacements: S. Parry, G. Thomas, G. Gajion, L. Ashley, S. Cross, S. Venter, T. Thomas-Wheeler, J. Hook.
Leinster: H. Keenan; C. Kelleher, J. O'Brien, C. O'Brien, J. Lowe; C. Frawley, J. Gibson-Park; P. Dooley, J. Tracy, M. Bent, R. Molony, S. Fardy, J. Murphy, S. Penny, R. Ruddock.
Replacements: S. Cronin, M. Milne, J. Aungier, J. Dunne, R. Baird, R. Osborne, H. Byrne, T. O'Brien.