Ulster captain Iain Henderson was sent off in the 75th minute but his side were deserved winners as Ospreys fell to an 11th defeat in their last 12 competitive matches in a 24-12 loss at the Liberty Stadium.
Henderson picked up a red card for charging into a ruck and making contact with the head of Dan Evans but by then Ulster were firmly in control of the match.
We need your consent to load this SoundCloud contentWe use SoundCloud to manage extra content that can set cookies on your device and collect data about your activity. Please review their details and accept them to load the content.Manage Preferences
Jacob Stockdale, Marcell Coetzee and John Cooney had scored tries for the visitors, with Cooney adding three conversions and a penalty.
Four penalties from Stephen Myler was Ospreys' response.
Ulster took a seventh-minute lead with a try from Stockdale. The away side declined a 35-metre kick at goal in favour of an attacking line-out and were rewarded when a succession of forward drives created the opportunity for Ian Madigan to send Stockdale over.
Cooney converted before Myler put Ospreys on the scoreboard with a penalty but the match continued to be shapeless, with neither side bringing any continuity to their game.
Poor kicks from Cooney and Stewart Moore went straight into touch to stop Ulster from building a platform, with Ospreys relying on predictable bursts from centre Kieran Williams to try and get some momentum into their play.
It therefore came as no surprise that the next two scores came via penalties from Cooney and Myler to leave Ulster with a deserved 10-6 interval lead.
After the restart a piece of magic from Stockdale enlivened proceedings. Deep in his own half, the full-back fielded a clearance before chipping over a defender and racing away. Ospreys looked in danger but Stockdale was hauled down and the move fizzled out.
However Ulster were not to be denied. Another powerful burst and excellent touch-finder from Stockdale secured his side a platform in the home 22 and from there the Ulster pack built up a head of steam to send Coetzee crashing over.
Cooney converted before Myler kicked his third penalty to keep Ospreys in contention as they trailed 17-9 going into the final quarter.
A scrum offence gave Myler the chance to succeed with another kick but the home side never looked like scoring a try and Ulster emphasized their superiority when Rob Lyttle ran strongly to create a try for Cooney.