The Dragons made an excellent start after kicking a penalty to the corner, going close with a driving lineout and then hammering away at the line before settling for a three-pointer by full-back Tom Prydie.
After 13 minutes Ospreys fly-half Dan Biggar managed to even the scores as he kicked a successful penalty kick over the posts.
The first try of the game came after a missed kick to touch from the Dragons. Ospreys fullback Dan Evans ran the ball back at the Dragons and it was Dan Lydiate who punched a hole in the defence, bursting through the line at pace before eventually being hauled down just a couple of metres out.
It was recycled well and after a series of pick and drives it was Tyler Ardron who went over for the score. Biggar converted to take the score to 10-3 with 32 minutes gone.
Prydie responded with his second successful penalty of the contest, but there was time left for Biggar to add another three points to the home sides score.
Half Time: Ospreys 13 – Newport Gwent Dragons 6
An early scrum penalty against the Dragons, on their own put-in on their 10m line, allowed Biggar to put three more points between the sides within four minutes of the restart.
Biggar once again slotted over a successful penalty, edging the Ospreys further into the lead.
But after a string of second half scrum penalties against the Dragons, referee Dudley Phillips lost patience and issued a yellow card to tight head Brok Harris.
At the next scrum the numbers were evened up as Scott Baldwin joined Harris in the sinbin after being penalised. Prydie went for goal from the resulting penalty but his long-range effort missed.
The Dragons went on to pressure the home side, going through the phases deep inside the Ospreys 22 which created a gap for scrum half Richie Rees to dart over. Unfortunately Prydie’s conversion struck the posts, leaving the score at 19-11 to the home team.
As the clock counted down it was the home side which rounded off the game with a simple penalty kick on the final whistle.
Full Time: Ospreys 22 – Newport Gwent Dragons 11
Ospreys Team: Daniel Evans, Richard Fussell, Ashley Beck, Josh Matavesi, Eli Walker, Dan Biggar, Rhys Webb; Duncan Jones, Sam Parry, Dmitri Arhip, James King, Alun Wyn Jones (c), Dan Lydiate, Justin Tipuric, Tyler Ardron.
Newport Gwent Dragons Team: Tom Prydie, Matthew Pewtner, Tyler Morgan, Jack Dixon, Hallam Amos, Jason Tovey, Jonathan Evans; Phil Price, Elliot Dee, Brok Harris, Andrew Coombs, Rynard Landman (c), Lewis Evans, Nic Cudd, Taulupe Faletau.
Attendance: 7,132
Man of the Match: Tyler Ardron (Ospreys)
Referee: Dudley Phillips (Ireland)