Edinburgh centre Nick De Luca was sent off for a dangerous tip tackle on Tom Grabham as the Ospreys secured a comfortable Rabo Direct PRO12 victory at the Liberty Stadium.
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De Luca saw red four minutes from time to add misery to the Scots as they slipped to their 10th straight defeat in all competitions.
Two tries from No 8 and man of the match Morgan Allen and one from scrum-half Rhys Webb were enough to see the Ospreys home. The Edinburgh try came from flanker Hamish Watson.
The win saw the Ospreys climb back into the play-off places even though they failed to gain a bonus point.
Ospreys skipper Kahn Fotuali'i swapped from scrum-half to wing to fill in the position left by Ross Jones' three-week ban for a tip tackle against Connacht.
That meant Webb and Matthew Morgan were named at half-back.
Edinburgh, who were forced into one late change with Andy Titterrell replacing injured hooker Steve Lawrie, included Wales internationals Richie Rees and John Yapp.
Edinburgh coach Michael Bradley named nine players aged 23 or younger as a consequence of international call-ups and injuries.
The Ospreys got on the scoreboard after only seven minutes when some good momentum up field ended with lock Jonathan Thomas putting over Allen for a try converted by Matthew Morgan.
Edinburgh's cause was not helped that fly-half Harry Leonard missed a penalty from 30 metres out and then De Luca knocked on just short of the left corner.
And with the visitors continuing to give away penalties the Ospreys scored a second try through Allen, who went over following pressure from a line-out. Fly-half Morgan converted to make it 14-0 after the first quarter.
The Ospreys continued to dominate and the only surprise was that they failed to add to their lead ahead of half-time.
Even more of a surprise was that Edinburgh scored a try in the final minute before half-time when openside flanker Hamish Watson went over after the Scots created an overlap on the left. Leonard added the extras.
Both Leonard and Morgan missed kickable penalty shots at the start of the second half.
But in the space of three minutes the Ospreys extended their lead to 24-7.
First Morgan kicked a penalty after Edinburgh centre Ben Atiga had been sin-binned before scrum-half Webb crossed for the third try, converted by Morgan.