Bath (9) 24
Tries: Cheeseman 2
Cons: Walshe
Pens: Walshe 4
Ospreys (18) 31
Tries: Vaughton, Hook, Terblanche
Cons: Connor 2
Pens: Connor
Drop goals: Connor, Terblanche, Hook
The Ospreys survived a second-half fightback to secure a fine win away to Bath in the EDF Energy Cup.
The visitors scored two tries to none in the first half, Jonny Vaughton and James Hook giving them an 18-9 lead.
Nick Walshe landed his fourth penalty for Bath after 47 minutes before Stefan Terblanche struck for the Welsh side.
Tom Cheeseman scored two tries in two minutes as Bath closed to within a point but drop goals from Terblanche and Hook wrapped up victory.
Bath took an early lead through a Walshe penalty but they struggled to build possession and the Ospreys, who were fielding a largely second-string side, threatened to pull well clear at half-time.
The Welsh raiders scored their first try when a long pass sent Vaughton over untouched in the corner for an unconverted try.
Walshe's second successful penalty edged Bath back in front but within a couple of minutes the Ospreys retook a lead they never relinquished.
Hook, 21, latched onto a kick and handed off two would-be tacklers before touching down wide on the right, with Connor converting.
The Ospreys fly-half added a drop goal and penalty to make it 18-6 after half an hour, but the visitors then lost scrum-half Jason Spice to the bin.
Walshe penalties either side of the break trimmed the gap to six points before Terblanche raced over from his own 22 after the Ospreys turned over possession from a Bath attack.
Connor converted but Bath then caught fire, with Cheeseman's quick-fire double and a conversion from Walshe making it 25-24 to the visitors with 20 minutes to go.
But after a rocky 20 minutes the Welsh side reclaimed control and drop goals from Terblanche and Hook wrapped up victory and made it two wins out of two for the Welsh side in group A.
"That we are out of the competition is one thing. What annoys me is the way we performed. We didn't seem to learn anything from last week's defeat at Bristol.
"Some players took on too much responsibility and we could have been more tactically aware."
"I'm damned if I do and damned if I don't - there are going to be a lot of upset players this week.
"I said to the players before the game that we had a team that knew how to win away from home."
Bath: Abendanon, Davey, Cheeseman, Maddock, Bory, Perry, Walshe, Flatman, Ward, Bell, Smith, Grewcock, Beattie, Scaysbrook, Goodman.
Replacements: Stephenson for Bory (40), Mangeolles for Perry (76), Barnes for Flatman (54), Mears for Ward (40), Short for Smith (50), Faamatuainu for Goodman (54). Not Used: Travagli.
Ospreys: Terblanche, Mustoe, Selley, Hook, Vaughton, Connor, Spice, James, B. Williams, Millward, Bateman, Evans, Beech, Tandy, Thomas.
Replacements: Parker for Selley (65), Griffiths for Millward (65), Powell for Bateman (76), A. Jones for Beech (48). Not Used: Bennett, Roberts, Byrne.
Att: 10,500
Referee: Dave Pearson (RFU)