The 2012 champions scored five tries in the bonus-point win as they made light work of a disappointing Edinburgh outfit who were second best throughout.
Richard Hibbard and Eli Walker both scored twice, with Jeff Hassler claiming the first try after just two minutes and Matthew Morgan completing the rout, while Dan Biggar added 12 points from the tee.
The Ospreys enjoyed the perfect start to their opening home game of the season as Canadian wing Hassler darted over following a powerful driving lineout - a weapon that was to regularly bring reward for the Welsh side.
Biggar added the extras 10 metres in from touch and he stretched the lead with his first penalty of the night after quarter of an hour when Edinburgh hooker Aleki Lutui lost his bind at a defensive scrum on his own 22.
With both sides struggling to keep hold of the ball in wet conditions, Edinburgh finally opened their account through a simple Harry Leonard penalty on 31 minutes after Hibbard popped up early at scrum time.
Ospreys flanker Tom Smith was carried from the field on a stretcher five minutes later with a suspected dislocated knee but any hopes of an Edinburgh comeback were severely dented in a five-minute spell either side of the break as first Walker and then Hibbard touched down to push the Ospreys 20 points clear.
Walker provided a fine finish after picking up Richard Fussell's pass one-handed a metre or so from the tryline after Greig Tonks had picked the wrong option in doubling up on Biggar rather than staying with his man.
Biggar could not land the conversion from just two metres in from the left but his side led 18-3 at half-time.
Walker went close to a second immediately after the restart but the Ospreys were soon celebrating once more as Hibbard rumbled over on the blindside following another secure lineout move.
Biggar missed from the tee for the second time in a row but Ospreys were 23-3 to the good after 42 minutes.
Edinburgh were at least next to trouble the scoreboard three minutes later when Tim Visser crossed for his 50th try in Celtic competition but that was as good as it got for the Scots.
The giant wing took Sean Kennedy's delayed pass to cut in between Alun Wyn Jones and Tipuric before powering through last-ditch attempted tackles from Fussell and Tito Tibaldi.
Leonard's simple conversion cut the gap to 13 points but the Ospreys put the game to bed when Hibbard and Walker again crossed in quick succession.
Justin Tipuric's yellow card for a tip tackle on Kennedy threatened to give Edinburgh a route back into the match but the hosts instead scored 14 points in his absence.
Hibbard made it 28-3 when Evans again won solid lineout ball close to the Edinburgh line on 53 minutes before Walker finished off the move of the match two minutes later.
The uncapped wing got on the end of Fussell's superbly weighted grubber kick following Ashley Beck's floated pass on halfway and, with Biggar converting both scores, the Ospreys led by 27 points with 24 minutes remaining.
Morgan's solo score put an even greater gloss on proceedings when he raced 80 metres with just seconds remaining.