Ulster's teenage wing Craig Gilroy scored a try in each half and his second touchdown, which began at a quickly taken line-out in the visitors' 22, turned the game on its head.
It also came in the middle of a 15 point burst from Ulster in the space of four minutes and set them on their way to a first bonus point victory of the season.
The defeat means the Blues lose their grip on third place in the Magners League table, Ulster moving ahead of them, and puts added pressure on next weekend's home clash with Glasgow Warriors.
Earlier in the weekend a last gasp try from replacement scrum half Jamie Nutbrown earned the Ospreys an important 16-15 victory over Connacht in Galwey. That triumph included a drop goal from the 18-year-old Matthew Morgan on his Magners League debut.
But there wasn't any luck for the Dragons in Ireland as they conceded four tries in a 27-6 defeat against Leinster in Dublin.