The Ospreys missed out on home advantage in the Guinness PRO12 play-offs as they failed to score in the second half of their 24-20 win over Connacht.
A bonus point try would have been enough to see the Welsh side finish in second spot above Munster, but they were unable to add to their three-try first half performance at the Sportsground.
That means Steve Tandy's men will have a return trip to Ireland when they visit Munster at Thomond Park in a mouth-watering semi-final next Saturday.
Just as table toppers Glasgow did in Galway three weeks ago, the Ospreys gave Connacht a lesson in creating opportunities and finishing them in the opening 40 minutes as Dan Biggar, Ben John and Rhys Webb all touched down.
However, with the wind behind them after the break, Connacht duly ate into their 24-0 deficit with Jack Carty kicking two penalties and Eoghan Masterson scoring a maul try.
A last-minute seven-pointer from Denis Buckley earned the Irish province a deserved losing bonus point. Their efforts over the season saw them secure a best-ever finish of seventh which sets up a European Champions Cup qualification play-off away to Gloucester next Sunday.
Determined to stay in the Champions Cup hunt, Connacht missed an early chance to break downfield as winger Matt Healy failed to hold onto Bundee Aki's offload, and the Ospreys gradually took control.
The visitors' scrum set up a monster penalty chance for Biggar and he took it with aplomb, splitting the posts from just inside his half.
Playing into the wind, Connacht struggled to make headway and they leaked the first try in the 15th minute when coughing up their own scrum ball. Number 8 Dan Baker's well-timed pass unleashed the Ospreys midfield and Biggar sent John crashing through before taking the return pass to go in under the posts and convert.
John turned try scorer 10 minutes later, Baker taking it up the field before Webb's flat delivery sent the outside centre through two poor attempted tackles from Buckley and Tom McCartney. Biggar turned it into a seven-pointer.
Eli Walker was next to threaten on a kick chase, Carty getting back to rescue the home side, but a classy break involving Dan Evans and Hanno Dirksen then laid on a try for the supporting Webb, who made a late trip to Galway following the birth of his second child yesterday.
Biggar's right boot made it 24-0 and Connacht dug deep to avoid a further concession before the interval, getting their reward with an early second half penalty from Carty.
Carty fired over his second penalty in the 49th minute with the Connacht pack finally building some momentum. They pressed from two lineout mauls in the Ospreys' 22, the second one producing a power packed drive that earned flanker Masterson a well-taken try.
Carty's successful conversion from the left closed the gap to 11 points, the home crowd urging the province on as John Cooney, Robbie Henshaw and Fionn Carr came more into the game.
The wind and rain of the final quarter saw the subdued Ospreys struggle for territory and Connacht, with retiring lock Michael Swift now on, kept pressing for scores.
At one stage on a dramatic final day, Pat Lam's charges were down to eighth in the table as Edinburgh edged ahead of Leinster at BT Murrayfield. But Leinster did Connacht a big favour by winning that game and Buckley bundled his way over from close range to give the westerners a further boost ahead of next week's play-off trip to Kingsholm.