The reigning RaboDirect PRO12 champions would have moved into the Play-off Zone had they won, but two yellow cards in the second half, and a stream of penalty successes from the boot of Gregor Hunter, made it a miserable trip north for the Welsh region.
Outside half Matthew Morgan scored all the points as the Ospreys raced into a 13-8 interval lead. The youngster kicked two penalties and converted his own try to give his side a chance of adding to their winning streak.
But Edinburgh, who hadn’t won in the competition since beating Zebre in September, tackled harder, ran stronger and completely dominated the second half proceedings in terms of territory and possession.
Hunter landed a penalty in the first half and then added five more after the break to add to a try by prop WP Nel. The Ospreys lost debutant prop Owen Williams three minutes after the break with a yellow card and then saw flanker Sam Lewis follow suit for not rolling away at a ruck after 68 minutes.
Morgan had a chance to level the scores to grab a second try with the scoreboard showing only a seven point gap, when he chased up a charged-down kick against his opposite number Hunter. But after picking up in the home 22 he was hauled down inches short and the Ospreys conceded a penalty soon after to lose their foothold.
The final insult came at the last scrum of the game in the shadow of their own posts when the referee penalised Duncan Jones for driving in and up as he wrecked the Edinburgh scrum. That gave Hunter the chance to take his tally to 18 points, and robbed the Ospreys of a losing bonus point.