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Ulster drew first blood at the Liberty Stadium with Paddy Jackson, a late replacement for Ian Humphreys, racing clear. The fly-half sliced in between Biggar and Andrew Bishop to beat the covering defence and score a try he then converted.
The Ospreys fly-half had the chance to hit-back but struck the uprights on five minutes. But from there Biggar made no mistakes and slotted four unanswered
penalties to hand his side a 12-7 lead at the interval.
Biggar continued his fine form with the boot in the second-half and he extended the hosts lead to 15-7 after Robbie Diack was sent to the sin-bin on 48 minutes.
And the Ospreys landed a decisive blow on the hour-mark with referee Dudley Phillips awarding penalty try following a succession of scrum re-sets, which
Biggar converted.
Richard Fussell put the result beyond doubt in the closing stages when he took advantage of an Ulster mix-up at the breakdown. Replacement fly-half Matthew Morgan slotted the conversion to give the hosts a 32-7 lead.
Ulster were awarded a penalty try of their own at the death but it was little more than a consolation.
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