For the Scottish outfit the first emotion was one of relief having last won a RaboDirect PRO12 game on September 14 against Zebre.
Gregor Hunter kicked 18 points while WP Nel crossed for a try, all of the Ospreys points coming from Mathew Morgan with a try, conversion and two penalties.
"We needed a win as quick as possible and, for 80 minutes, the guys toughed it out," said Bradley.
"Ospreys came here on the back of five successive wins, and we needed to get stuck in. The defence was magnificent.
"We seemed to be sharper today, when the ball went to deck there was an Edinburgh Rugby player there and that was great to see.
"The crowd were right with us at the end when we needed them and hopefully this will be a sea-change in terms of results.
"We got something back today- that was the challenge for the boys who took to the pitch tonight, and I'm pleased to say the players earned a well-deserved win."
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