Steve Tandy's side have defeated the Scarlets 23-16 to take their first win of the season.
The Ospreys went into half-time at Parc-Y-Scarlets with a 9-6 lead after three Dan Biggar penalty kicks.
Tries from Ryan Jones and winger Hanno Dirksen in the second half made Steve Tandy's side sure of the win, before Scarlets flyer George North crossed to secure his side a bonus point score.
Prop Duncan Jones was named man of the match for his efforts, which saw the Ospreys enjoy a much improved performance.
The win has moved the Ospreys, the defending Pro 12 champions, up to 8th in the league standings, with Simon Easterby's side still topping the table after securing the losing bonus point.
Speaking after the win, Ospreys forwards coach Jonathan Humphreys said:
"We never felt we were the worst team in the world after losing our first three games".
"There were a few things that didn't go our way, but we got a bit more physical today than we did in those first three games".
"We don't feel that we are perfect at the moment, we just feel that we ground out a good win against a good team".
The Ospreys will look to build on the win next weekend when they welcome Munster to the Liberty Stadium, whilst the Scarlets face a tricky away trip to Treviso.
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