The Welshmen have been away on their travels so far this season, but boosted by the return of skipper Alun Wyn Jones, in his first appearance of the season, alongside fellow Lions Adam Jones, Hibbard, and Ian Evans and Justin Tipuric it was a six-try romp.
Jeff Hassler marked his first start for the region with the first try of the game with only three minutes on the clock, the winger diving over after a well-worked wrap around move from a rolling maul.
Dan Biggar added the conversion and two more penalties from the Wales fly-half meant that the hosts were 13-0 to the good with less than 20 minutes on the clock.
Harry Leonard responded with a penalty of his own to finally get the visitors on the board around the half hour mark.
But before half-time Walker skipped clear down the left wing and the Ospreys were in total control, Biggar missing the conversion but his side went in 18-3 up at the break.
Any hopes Alan Solomons might have had of turning the game around after the interval at the Liberty Stadium soon disappeared when Hibbard barged over in only the 42nd minute to make it 23-3.
The Scots needed a response and they got it when Tim Visser came in off his wing to burst through a gap and motor over for the Scots' first try of the night, Leonard adding the conversion for 23-10.
But that was about as good as it got for Edinburgh as, despite Tipuric being sent to the sin bin for his involvement in a scuffle, Hibbard crossed for his second try and the bonus point score for Steve Tandy's men.
Walker then got back in the action, finishing of a fine team move to grab his second and with Biggar converting both scores it was now 37-10 to the hosts.
Both sides emptied their benches with the result now a foregone conclusion and it was an Ospreys replacement Matthew Morgan who had the final say.
The 21-year-old, on for Biggar at fly-half, made a bursting run from deep and his momentum carried him over the try-line in the left corner before he dusted himself down to add the conversion and seal an impressive victory.
|Ospreys Score Card|
|Edinburgh Rugby Score Card|