Ulster triumphed 21-7 over the Ospreys at the Kingspan Stadium but failed to secure the bonus point that would have heaped maximum pressure on Conference A leaders Leinster.
The four points put Dan McFarland's side one point behind defending Guinness PRO14 champions Leinster ahead of next week's crunch clash between the sides in Belfast, though the Dubliners play on Sunday.
After being put under huge pressure by a spirited Ospreys outfit, Ulster roared back in the second half through a score from John Andrew and a penalty try and were unlucky not to get over for a fourth touchdown, with Rob Lyttle having three efforts ruled out.
Ulster, even with Jacob Stockdale back from injury, had looked down and out in the opening half against a determined and accurate Ospreys effort which was kicked off by Keelan Giles' first minute try.
But in the closing minutes of the half, Nick Timoney set John Cooney up for a score totally against the run of play, with Cooney's conversion tying things up at 7-7 and effectively changing the course of the game.
The Ospreys had the ideal start when Ian Madigan was charged down by Rhys Webb and Giles won the foot race to the line. Stephen Myler converted the score.
Webb nearly created another for the Ospreys with a searing break down the blind side before Ulster scrambled to plug the gap and survive.
That was the pattern for the remainder of the half, with the Ospreys piling on the pressure by dominating possession and territory while putting Ulster firmly on the back foot, especially in the scrum, where Gareth Thomas did notable damage.
Ulster looked shell-shocked in the face of the Ospreys' dominance, but then, in the 37th minute, Tiaan Thomas-Wheeler's attempted chip deep in the home side's territory was blocked, allowing Timoney to pick up and break.
Timoney's pass found Cooney on his outside and the scrum-half ran it in, with Dan Evans pulling up with an injury. Cooney then converted to tie the scores just as the half ended.
The score certainly revived Ulster, who began the second half with energy and belief, though again their accuracy looked off in the opening stages with errors from Cooney and Michael Lowry.
But Ulster battled their way back and, after going to the corner twice, a driving maul saw Andrew dot down in the 54th minute.
Cooney again converted and Ulster now led 14-7.
Two minutes after the hour a Lyttle pass to James Hume was deliberately knocked on by Evans and referee Sean Gallagher awarded Ulster a penalty try, while yellow-carding the Ospreys' full-back.
However, Ulster failed to score any more points in the remainder of the game, even though Lyttle got over three more times with each one ruled out.