The Scarlets were pipped in Connacht and runaway leaders Munster were overturned in Treviso, so the Ospreys needed to make the most of the weekend by closing the gap on the front runners for the four Play-Offs places on the road to the second Magners League Grand Final on Saturday, 28 May.
The four points looked a long way off after Ian Humphreys had given Ulster a 13-0 lead with two penalties and then a penalty try which he also converted. In much the same way as they had blown away Cardiff Blues on their last visit to Wales, when they ran out 37-15 winners, Ulster scored at almost a point a minute in the opening quarter to create what looked like being a winning platform.
But after that bright opening the Ospreys scrum began to turn the screw and the penalties flowed as the Ospreys finally got their act together.
That allowed Biggar to prove he can still hit the mark with his goalkicking as he landed six out of eight attempts to punish the visitors. One of his penalties was a monster from 55 metres on the stroke of half-time that gave the home side the lead for the first time at 14-13.
As well as Biggar's three penalties the Ospreys also conjured up a corner try for ex-All Black flanker Marty Holah which owed much to the skill and vision of Ashley Beck, who threw a long, cut out pass to create the opening.
Two silly home indiscretions at the start of the second half allowed Pienaar, who took over at outside half from Humphreys when he left the field with a shoulder problem after 31 minutes, to show off his considerable goalkicking skills and Ulster suddenly found themselves five points clear.
But Biggar replied with three more penalties, two for scrum offences, and not even a third strike from Pienaar six minutes from time could claw back the deficit.
Scorers: Ospreys: Try: M Holah; Pens: D Biggar 6. Ulster: Penalty Try; Con: I Humphreys; Pens: R Pienaar 3, I Humphreys 2