The win came while head coach Steve Tandy was at home in Wales with his wife as they waited for the birth of their latest child and despite having a Jeff Hassler try ruled out by referee Neil Hennessey.
Three second half penalties from Dan Biggar hauled the Welsh region over the line after they had led in the first half thanks to a Hassler try and conversion that overtook an early try from home wing Gerhard van der Heever.
Biggar and Ian Keatley swapped penalties to leave the visitors leading by two points at the break, 10-8, but it was the Welsh outside half who won the kicking duel in the second half with three successful kicks to the Irishman’s two.
The Ospreys now lead the table on try count from the only other unbeaten team, Glasgow, and they both have a five point gap over third placed Ulster.