Munster drew first blood at the Liberty Stadium with an Ian Keatley try within two-minutes but it was the Ospreys that delivered the knockout blow with a dominant performance to reach the showpiece final.
Biggar, Kahn Fotuali’I, Hanno Dirksen, Andrew Bishop and Rhys Webb all touched all down as the Ospreys ran riot. They will not face either Leinster or Glasgow Warriors in the PRO12 final.on May 26.
The Ospreys got off to a nervy start at the Liberty Stadium and found themselves trailing inside two minutes as Munster came flying out of the blocks.
Lifeimi Mafi released Ireland international Keith Earls, who sliced through the Ospreys defence before sending Keatley over for a converted try.
But the Ospreys fought back and Biggar slotted a penalty on eight minutes, before grabbing a try to take the lead.
After a Shane Williams try was disallowed for a foot in touch, the Ospreys snatched possession at the lineout and launched a sustained assault on the Munster line.
Biggar fed Ryan Jones and wrapped around the Wales star to collect a superb offload out of contact and score. The fly-half slotted the simple conversion and exchanged shots at goal with Keatley as the Ospreys kept their noses in front.
The Swansea-based outfit were fortunate not to pay for a succession of errors on their own try-line as half-time approached. But where Munster failed to take their opportunities, the Ospreys demonstrated plenty of killer instinct.
From deep inside their own half Richard Fussell raced outside Mick O’Driscoll and took full advantage of a Simon Zebo slip to release Joe Bearman.
The former Newport Gwent Dragons man sucked in the defence to send Fotuali’I clear for the decisive try, which Biggar made no mistake in converting.
Biggar continued his virtuoso performance in the second-half and broke the 1000-point milestone for the Ospreys.
Steve Tandy’s men landed the killer blow on 55-minutes with Dirksen’s try. Justin Tipuric did the damage with a thunderous hit and turn-over on Ronan O’Gara, and the ball was spread through the hands for Richard Fussel to put Dirksen over in the corner.
With Munster out on their feet under a physical onslaught , the Ospreys continued to wreak havoc and they grabbed further devastating tries Bishop and Webb to cap a comprehensive triumph.
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