The Ospreys had built a 9-6 lead at the interval thanks to three penalties from Shaun O'Conner, with Ulster responding through two successful kick from Paul Steinmetz.
Ulster looked to be wrestling the advantage in the early stages of the second half, but after spurring a straight forward kick at goal in favour of an unsuccessful catch and drive in the corner the feeling was there that this may not be the Irish side's night.
Steinmetz finally levelled the scores for a third time on 57 minutes however only 2 minutes later The Ospreys were gifted the only try of the game when scrum-half
Spice cleaned up a scrappy scrum and made a break down the line.
He chipped over the defence, but came out second best in a foot race with
Campbell Feather, but the Ulster flanker was unable to control the ball on the wet surface, and Spice took advantage by getting the touchdown.
Steinmetz reduced the visitors' lead to two points with his third successful penalty, but it was the Ospreys who finished the stronger.
Connor was gifted three more points when Maxwell was caught offside, and the visitors' out-half sealed victory in injury time with a drop goal.
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