Early indiscipline from Edinburgh allowed Dan Biggar give the Ospreys a handy cushion before theyscored a try in each half from flanker Justin Tipuric and winger Richard Fussell.
The Ospreys welcomed back internationals Alun Wyn Jones, Ryan Jones, Andrew Bishop and Nikki Walker to their starting line-up, while Adam Jones, Mike Phillips, James Hook and Tommy Bowe bolstered the bench.
Edinburgh coach Rob Moffat made six changes to the side that beat Connacht last time out, with Welsh centre David Bishop making his first start for the club and fly-half David Blair and prop Kyle Traynor winning their 50th caps.
The Ospreys won a succession of early penalties and with a place-kicker of the quality of Biggar, he needed no second invitation. They were dominant in the loose, with hooker and man-of-the-match Richard Hibbard hungry for work.
Biggar converted five penalties inside the opening quarter, with one of them close to the halfway line. That gave the Ospreys a 15-3 buffer, with Chris Paterson's fifth-minute penalty the sole response from the visitors.
Paterson had to go off before the end of the first half with a dead leg, and by that stage Edinburgh were 22-9 behind.
The Ospreys' early lead was boosted by a try for blindside flanker Tipuric who was put away down the right flank by prop Duncan Jones.
The 21-year-old Tipuric chipped ahead and impressively sidestepped the cover to run in his first ever league try. Biggar converted to extend the Ospreys lead to 22-3 after 24 minutes' play.
Edinburgh reduced the deficit, before the interval, with two David Blair penalties and the Ospreys suffered a blow early in the second half when Ryan Jones was yellow carded for a dangerous tackle on Edinburgh scrum half Mike Blair.
But despite being down a man, the Ospreys grabbed the first points of the half when Biggar converted his sixth successful penalty.
And after the Ospreys introduced their big guns - Phillips, Hook and Adam Jones - they pinned Edinburgh back and went in search of more scores.
Though they initially failed to get a second try, Biggar increased his points tally to 23 points with a drop goal on the hour mark.
And with Edinburgh themselves reduced to 14 players with Alex Grove's 68th-minute sin-binning, Ospreys replacement Jonathan Thomas was held up over the line.
But the try soon came courtesy of a quickly-taken penalty. Philips tapped it and Barry Davies' flicked pass led to Fussell going over in the left corner for his fifth touchdown of the current campaign.
With the game over as a contest, Edinburgh, who brought on John Houston for his 50th Magners League appearance, at least got in for a consolation score.
Their danger man Tim Visser went over in the closing minutes, profiting from a brilliant behind-the-back pass from Jim Thompson, to continue his incredible scoring run. Visser has now scored eight tries in nine league games this season.
The Ospreys finished out the game with 14 players on the pitch, as replacement Ian Gough was sin-binned for an off-the-ball incident. But the Welshmen were soon celebrating only their second win in seven meetings with Edinburgh.
Commenting afterwards, man-of-the-match Richard Hibbard said: "It was an excellent result on the back of two other strong Magners League wins when the Wales squad was away.
"They are great results to build into Europe. In patches we were awesome, especially in the first 20 minutes when we kept building and taking points.
"I'm just happy to get some game-time. It's been pure conditioning for the last five weeks, but it seems to have paid off."
|Ospreys Score Card|
|Edinburgh Rugby Score Card|