The hosts never hit top gear, although a try midway through the first half from centre James Hook gave them some hope.
Shane Williams scored an excellent second half try but there was little else for Holley and his management team to take from the performance.
The Dragons, who are challenging the Scarlets and Cardiff Blues for automatic Heineken Cup qualification, led 12-11 at half-time.
Former Osprey Shaun Connor kicked all of the visitors' points, landing six of his seven penalty attempts, but a late drop goal from Hook robbed them of a losing bonus point.
Dragons boss Paul Turner made four changes to the side that beat Connacht 27-14 at Rodney Parade on Sunday, with Connor coming in at fly-half, Rory Sidey at centre, Steve Jones at hooker and Jamie Ringer in the back row.
Captained by Wales lock Luke Charteris, the Dragons were gunning for their first away win since January and their first ever 'season's double' over their neighbours to the west.
When the sides met at Rodney Parade in December, tries from Jason Tovey, Rob Lewis, Rhys Thomas and Gareth Wyatt helped the men of Gwent to the 30-24 win.
The Ospreys, who suffered a two-point defeat in Edinburgh last weekend, included all six of their 2009 Lions for this midweek clash.
Hook was selected in the unfamiliar position of outside centre, with youngster Dan Biggar donning the number 10 shirt.
Flanker Tom Smith got a rare start, while teenage scrum half Tavis Knoyle made his debut as a second half replacement.
Two successful penalties from Connor, sandwiching a Biggar drop goal, had the Dragons 6-3 ahead before Hook pounced for his 18th-minute try.
The Dragons were on the front foot for much of the first quarter, but Biggar's pinpoint kick out to the right was collected by Tommy Bowe and the Irishman passed on his outside for the supporting Hook to ghost over for the score.
Hook missed the conversion attempt but followed up with a well-struck penalty to move the Heineken Cup quarter-finalists into a 11-6 lead.
Connor missed an initial chance to respond and the Dragons had cause for concern just a minute later when Ringer was sin-binned for poor challenge as he took Lee Byrne out in mid-air as the Ospreys full-back jumped for a high ball.
However, going down to 14 men seemed to drive the Dragons on and Connor kicked two late penalties after Hook had missed one to leave the visitors ahead for the break.
Byrne was actually withdrawn at half-time as a precaution, following a slight knock to his knee.
On the resumption, the Ospreys' night was not getting much better when Hook had his third missed kick of the game.
But an inspiring break in midfield from Andrew Bishop roused the Ospreys into action and from the resulting ruck, the Dragons lost Rory Sidey to a yellow card for killing the ball.
Hook duly bisected the posts with the penalty, edging the Ospreys into a 14-12 lead, but the Dragons wasted little time in replying through Connor.
Then on 55 minutes, Shane Williams scorched through for what proved to be a decisive try.
He stepped his way past Rhodri Gomer Davies and cantered over under the posts, with Hook adding the extras for a 21-15 scoreline.
Connor split the Ospreys defence, moments later, and the Dragons were denied a probable try when Bishop cleared the support runners with an off-the-ball tackle.
He saw yellow for the challenge and Connor landed the resulting place-kick before he was off target with a snap drop goal attempt.
An infringement from Aled Brew helped Hook kick the Ospreys onto 24 points but with time running out, the hosts' push for further tries disappointingly never came. In the end, Brew came closest to scoring a late try.
And the title race was as good as over as Hook missed his fifth kick at the posts and he then popped a drop goal through the uprights, with four minutes remaining, to close out the scoring.
The Ospreys' 10th win of the league campaign leaves them ten points behind Munster with two matches remaining, including a meeting in Limerick between the top two.
But, under Magners League rules, if Munster lose their final two games and the Ospreys pick up two bonus point wins, Tony McGahan's side will still lift the title on May 15 courtesy of their number of wins (13 so far).
Speaking afterwards, Ospreys coach Sean Holley said: "It's very disappointing. It would have been tall order - we needed three bonus point wins in our last games - but we're just happy to get a win in the end, really.
"We are trying to build some confidence, some momentum towards the end of the season.
"It clearly wasn't a night for tries and the Dragons made it really, really difficult for us. But we got the win and we'll look to get two more wins to finish the season of strongly.
"We want to go to Munster in the last game and prove a point and we'll just keep working because there's another season to play for."
