But the Welsh team were beaten to the semi-finals by Exeter who won 35-7 at Bristol to top Pool 2.
Jay Baker went over twice for the visitors with Kieron Fonotia and Hanno Dirksen also touching down.
But Ospreys' hopes of reaching the knock-outs did not materialise, ending Welsh interest in the 2016-17 cross-border competition.
Ospreys ended their Anglo-Welsh Cup campaign with a bonus-point win at Wasps.