Lyn Jones's outfit, narrow losers to Munster last week, got back on track in their double aim to secure Heineken Cup qualification for next season and finish as the highest placed Welsh team in the league.
For the Dragons, this loss pushed their winless streak to seven games. Their loose head prop Adam Black did become the first player to appear in 100 league fixtures but otherwise it was a night to forget for the visitors.
The Ospreys were without Wales duo Gavin Henson (ankle) and Mike Phillips (knee) but still fielded a strong line-up that included Welsh wing wizard Shane Williams, who missed a last-gasp drop goal attempt against Munster.
The Dragons made four changes to the side that lost to Connacht at home seven days ago, with the experienced Kevin Morgan reinstalled at fullback. Up front, Paul Turner plumped for Ben Daly at hooker, Andrew Hall in the second row and the fit-again Richard Parks in the back row.
The visitors made a fifth change before kick-off when the 18-year-old Jason Tovey was parachuted in at fly half for rib injury victim Ceri Sweeney. Tovey, who was making his senior debut for the region, opened the scoring for the Dragons by left-footing a seventh-minute penalty through the posts after the Ospreys had strayed offside.
Up the other end, James Hook replied, three minutes later, with a straightforward penalty from in front of the posts.
Tovey, who had 'a really positive debut' according to coach Turner, was unfortunate not to land a drop goal but his effort struck an upright and the Ospreys regrouped. The home side were having the better of possession and territory but the Dragons were frustrating the EDF Energy Cup winners who struggled with their finishing.
Johnny Vaughton was almost away for a try on the left wing, yet Dragons fullback Morgan deliberately knocked on to prevent Lee Byrne's pass getting to Vaughton. The resulting penalty was missed by Hook and the number 10 missed his third effort on goal just a few minutes later.
The Ospreys then lost winger Williams to a dead leg. However, their chances of breaking the try deadlock were boosted when Dragons flanker Parks was sin-binned on the half-hour for tackling Marty Holah without the ball.
Try as they might, the Ospreys just could not force their way over the visitors' try line and they had to settle for Hook's second penalty success in the 37th-minute.
6-3 ahead at the interval, Jones's men almost put Andrew Bishop over for the opening try five minutes into the second half but the centre was knocked into touch by a solid tackle from Rhodri Gomer Davies.
Both sides struggled to gain momentum after the restart and a 12-minute stoppage for a worrying injury to Gomer Davies, who was left shaken after an attempted tackle on Filo Tiatia, took some bite out of the game. The Dragons centre, who was stretchered off in a neck brace, thankfully came around in the dressing room and viewed the remainder of the game from the visitors' bench.
The Ospreys stretched their lead, coming up to the hour, when scrum half Justin Marshall cheekily nudged a drop goal through the posts. Luke Charteris then saw yellow for a late tackle on Hook as the Ospreys fly half chased his own chip kick.
The Dragons were really up against it now and their valiant defence gave way in the 72nd-minute when Williams's replacement Aled Brew completed a slick attacking move. However, there seemed to be a forward pass in the lead-up to the try as Hook's delivery to Lee Byrne, who provided the final assist, looked decidedly forward.
Dragons boss Turner was particularly annoyed that referee Tim Hayes and his match officials had missed the forward pass and Hook rubbed salt into the visitors' wounds by nailing the conversion from far out on the right.
That seven-pointer gave the Ospreys enough of a cushion to see out their fifth win in their last six encounters with the Dragons. It also denied the Newport Gwent side a deserved losing bonus point and it could possibly prove crucial as they look to finish ahead of both Ulster and Connacht in the lower reaches of the table.