The Irish side, who had opened their season with a home win over Galsgow Warriors, were able to bring on five players who had helped them reach the Heineken Cup last season as the game wore on and finished the stronger.
A try by wing Hanno Dirksen midway through the first-half seemed to have put Alun Wyn Jones’ side on the road to victory. Outside half Matthew Morgan added a conversion and two penalties to make it 13-3 after 52 minutes and everything seemed on course for the champions.
But as new Ulster coach Mark Anscombe brought on his cavalry, so his side grew strong and with the likes of Stephen Ferris, John Afoa, Tom Court, Paul Marshall and Andrew Trimble taking centre stage, so the challenge mounted.
Afoa and Marshall figured prominently in the move that led to the match winning try for the Ulster scrum half five minutes from time. Young outside half Paddy Jackson, who fired over two penalties as well, added the conversion to make victory complete.
Scorers: Ospreys; Try: H Dirksen; Con: M Morgan; Pens: M Morgan 2
Ulster: Try: P Marshall; Con: P Jackson; Pens: P Jackson 2, N O’Connor
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