Sam Davies kicked four penalties for the visitor, who put the home side under enormous pressure at times, and it took three kicks apiece from Ian Madigan and Jimmy Gopperth to see the champions through to an 18-12 triumph.
It was only the second defeat of the season for the Welsh region in the competition and Munster’s home win over Ulster allowed them to take over at the top. They have 32 points to the Ospreys’ 31.
With 19 players unavailable through injury or international duty Ospreys head coach Steve Tandy was stretched to the limit in selection, but still had plenty to feel proud about at the end of the game.
Davies’ first penalty gave the visitors the lead, but that was the only time they led. It was 9-9 at the break and Gopperth’s three second half penalties out-did Davies’ one extra for the Ospreys.