Tries by Shane Williams and James Hook booked the Ospreys a place in the Magners League Grand Final in a hard-fought last four clash against Glasgow at the Liberty Stadium.
But a crowd of only 7,079 watched the Ospreys reach the showpiece on May 29, where they will play the winners of the other semi-final between Munster and Leinster tonight.
Glasgow have never won on Ospreys turf and they were not helped that Dan Parks missed eight points' worth of kicks, failing with two penalties and missing the conversion for Fergus Thomson's second-half try.
The Warriors were without Scotland captain Chris Cusiter against an unchanged Ospreys. Mark McMillan took over at scrum-half.
The Ospreys took a narrow 7-0 lead into half-time. Alun Wyn Jones, who was making his 100 appearance for the Ospreys, stole an early lineout. But solid Scots' defence forced Dan Biggar into a drop-goal attempt which he pushed wide.
But on 10 minutes the Ospreys had their first try. Glasgow knocked on in contact on the halfway line, Shane Williams picked up and ran in unopposed for only his third regional try of the season.
The Ospreys had the better of the referee's decisions but what penalties Glasgow had Parks missed with long range efforts on 14 and 34 minutes.
The only other try scoring chance of the half came in injury time when Andrew Bishop charged down a Parks kick, but the Ospreys centre knocked on.
The second half began in dramatic fashion with Glasgow scoring a try. Hooker Bernard Thomson went over in the left corner after scrum-half Mark McMillan had picked up a loose palm down at a line-out from Ryan Jones.
But in the space of three minutes the Ospreys were back in control of the contest leading 17-5. A Biggar penalty was followed by a fine try from James Hook, who made a fine break down the left and then chipped over the cover defence to regather and go over.
After that the Ospreys took full control of the game and put some gloss on the scoreline with an injury time penalty for Biggar.