Edinburgh (26) 32
Tries: De Luca, Cross Cons: Paterson Pens: Paterson 5
Drop Goals: Godman
Ospreys (6) 16
Tries: Walker Cons: Jarvis Pens: Jarvis 3.
Ospreys Marty Holah gets tackled by Edinburgh's Allister Hogg
Edinburgh survived a second-half scare to see off a strong challenge from a depleted Ospreys at Murrayfield.
Back-row pair Ross Rennie and Ally Hogg inflicted the initial damage before Nick de Luca dived over in the corner.
Matthew Jarvis landed three penalties and prop Geoff Cross claimed the second try of the evening before half-time.
Nikki Walker sped over for a top-notch try after a sizzling handling sequence, but the Ospreys revival ended as Chris Paterson sent over his fifth penalty.
The result was a confidence boost for Andy Robinson's side in the build-up to the Heineken Cup double-header against Wasps.
At times Edinburgh made heavy weather of a team who were missing many of their frontline stars.
Robinson's men got off to a bright start with barely 60 seconds on the clock when Rennie and Hogg combined before De Luca plunged over.
Paterson calmly added the extra points to leave the Ospreys stunned.
The home side retained the upper hand, although they lost some ground when Matthew Jarvis landed a penalty to claw back three points for the visitors.
Paterson replied in identical fashion and his penalty duel with Jarvis continued as the visiting marksman kept the margin to four points.
It was end-to-end action and Edinburgh stretched their advantage again midway through the half as Phil Godman clipped over an opportunist drop goal.
And Paterson struck again almost immediately to open up a useful 10-point cushion.
He completed his treble six minutes later to put the capital side firmly in control.
Edinburgh stepped up the tempo as half-time approached and they delivered a further dent to the Ospreys when prop Cross claimed the second try from yards out, which was converted by Paterson.
The Ospreys opted to go for goal with a penalty four minutes after the break, and Jarvis notched his treble to keep their slim hopes alive.
There was more to come for the Welsh side when Walker scorched over for a quality try after a smooth handling sequence involving at least six men and Jarvis added the conversion to heap more pressure on.
And there was further trouble for Edinburgh when Cross was yellow-carded for side entry at the breakdown.
But the night was over for the Ospreys when Paterson banged over his fifth penalty.
Edinburgh: Paterson, Robertson, Cairns, De Luca, Webster, Godman, M. Blair, Jacobsen, Ford, G. Cross, C. Hamilton, Gissing, MacDonald, Rennie, Hogg, Newlands.
Replacements: Southwell for Robertson (54), D. Blair for Cairns (60), Laidlaw for M. Blair (78), Kelly for Ford (78), Mustchin for C. Hamilton (68), Newlands for Rennie (54), Kerr for Newlands (63).
Ospreys: Bowe, K. Phillips, D. Bishop, Parker, Walker, Jarvis, Webb, James, Shervington, Mitchell, Tiatia, Bateman, Tandy, Holah, Smith.
Replacements: Beck for D. Bishop (68), Wells for Webb (53), Breeze for James (79), Bevington for Shervington (79), Griffiths for Mitchell (41), Garfield for Bateman (80), Thomas for Smith (44).