Jonny Vaughton (left) scored one of the Ospreys' tries
Edinburgh (7) 12
Tries: Mustchin, Cairns
Ospreys (10) 30
Tries: Vaughton, Tandy, Terblanche, Marshall, Bennett
Edinburgh's dream of bringing the Magners League title to Scotland for the first time was clinically demolished by the streetwise Ospreys.
Matt Mustchin touched down to give the under-strength home side a deserved lead, with Duncan Hodge converting.
But tries from Jonny Vaughton and Steve Tandy and a penalty and try from Stefan Terblanche put Ospreys in control.
Justin Marshall and Huw Bennett added further tries for the visitors, with Ben Cairns replying for Edinburgh.
Home coach Lynn Howells had expressed confidence that his side could stay in touch at the top despite the loss of several Scotland internationals.
But they could find no answer to the pace, power and know-how of the Neath-Swansea combine, superbly orchestrated by former All Blacks scrum-half Marshall.
Veteran stand-off Hodge controlled matters in the first quarter with a variety of accurate positional kicks.
But he missed a penalty chance before a 25th-minute touchdown by utility forward Matt Mustchin, who broke away at a line-out and wheeled over the line.
Hodge confidently banged over the conversion, but Ospreys made a stirring reply.
Tom Smith hauls back Edinburgh's Lucio Lopez Fleming
First - also from a line-out close to the corner - the ball was flashed across the field for Jonny Vaughton to finish in style.
And flanker Steve Tandy picked up a simple second try when he was left unmarked on the left.
Terblanche stretched their lead with a penalty after the break.
And the former Springboks star returned to the spotlight with a try after a poor challenge by Phil Godman allowed Sonny Parker to supply the pass.
Spice slotted the conversion to leave Edinburgh trailing by 13 points with time slipping away.
Marshall turned on the pace and power to make sure of the valuable bonus point.
Cairns clawed back a touchdown for the hosts, but the Ospreys had the last word when substitute hooker Bennett ploughed over.
Ospreys director of rugby Kevin Hopkins:
"Jason Spice and Stefan Terblanche had trouble with the goal kicking so we had to do it with tries, and it was great to get the bonus point.
"Having Sonny Parker and Filo Tiatia back was fantastic and Matthew Jones came on towards the end - they got better as they got more game time.
"We needed that first league away win of the season, but there are a lot more away trips in the run-in so we'll need to keep that up."
Edinburgh: Warnock, Dey, Cairns, Jorgensen, Lopez Fleming, Hodge, Laidlaw, Jacobsen, Kelly, G. Cross, Mustchin, Bentley, Strokosch, MacDonald, S. Cross.
Replacements: McCall for Dey (66), Godman for Jorgensen (50), Senio for Laidlaw (58), Hewett for G. Cross (74), Rennie for Bentley (69), Pringle for S. Cross (55). Not Used: Lawrie.
Ospreys: Terblanche, Vaughton, Parker, A. Bishop, Mustoe, Spice, Marshall, James, B. Williams, A. Jones, Cockbain, Thomas, Lloyd, Tandy, Tiatia.
Replacements: Walker for Vaughton (69), M. Jones for Spice (78), D. Jones for James (58), Bennett for B. Williams (54), Griffiths for A. Jones (62), Powell for Lloyd (72), Smith for Tiatia (78).
Referee: Peter Fitzgibbon (Ireland)