The Ospreys were denied an injury-time try by the TMO as Munster advanced to the Pro12 Final, winning 21-18 at Thomond Park.
Simon Zebo struck first blood on the brink of half-time with a well-timed try, before Denis Hurley then went over the other side of the break to put Munster on the brink of the final.
But Ospreys' Rhys Webb fired back minutes later to put his side back in contention.
Paddy Butler though went over moments later, for the third try in less than ten minutes to again put Munster way ahead.
Jeff Hassler again narrowed the gap with the game's fifth try, but despite the kicking efforts of Dan Biggar, the Ospreys couldn't turn the scoreline around and it's Munster who will meet Glasgow at Ravenhill.
It was Ospreys who made most of the early running, Biggar going close with a drop goal effort inside the first two minutes.
They followed up that bright start for the next few minutes and took a three-point lead from the boot of Biggar, who capitalised after Munster were penalised for failing to roll away.
Munster were able to level soon after though, with Ian Keatley kicking his first penalty of the afternoon and minutes later the number ten sent the hosts into the lead with another perfectly executed kick.
As the half edged on, neither side were able to put together a legitimate attempt to reach the try line, as both defences doggedly held up the others attack.
The hosts were able to steal the ball on Ospreys' 22, but again couldn't find a way past in an evenly matched opening half hour.
Keatley was presented with his third kick at goal with the clock approaching half-time, but this time squandered the chance as the ball sailed just to the left of the sticks, keeping the lead at just three.
But with just over a minute to go until the break, Munster crucially struck. Following a scrum, some quick interchange between Keatley and CJ Stander eventually found Butler and his final pass to Zebo allowed the winger to touch down right before the break.
Keatley missed the chance to stretch the lead to ten, but Munster took a vital eight-point advantage into half-time.
The second half started in the worst possible way for Ospreys, who came out looking to avenge that last-minute try.
Munster instead doubled their try tally and potentially off killed any chance of Ospreys progressing. Following a maul, Keatley's searching ball out wide was well caught by Hurley, who expertly stayed in touch and touched down just inside the corner, though once again Keatley missed the opportunity to add the extras.
But despite those two setbacks, Ospreys dragged themselves right back into contention with the third try in just over five minutes of play.
Webb was able to rob the ball from the back of Munster's scrum and leap forward for the line to add a new air of excitement into a contest which the Irish province were threatening to run away with. Biggar continued the tradition of missing conversions however, meaning Munster did still have an eight-point advantage.
Ospreys' hopes were again dashed after that try though, with Butler finishing off a quick break following an Ospreys breakdown after Duncan Williams had set him free. Keatley missed again, and the intense nature of this second half quickly produced the games fifth try.
Jeff Hassler came in from his wing and found a gap in the Munster backline just wide enough for him to nip through, Biggar converting to put the gap back down to just six points.
The Welsh side, who already had beaten Munster twice this campaign, continued to throw everything forward in the search for what would be a game-changing third try, and when Biggar was handed the chance to kick three more points, he duly obliged to make it a three-point game with less than 10 minutes to play.
Keatley could have restored those three points, but once again missed an opportunity to kick through to keep the scores tight.
A change of kicker still produced the same result a minute after, JJ Hanrahan missing after taking over the duties.
The final second saw Ospreys finally cross the line for the third time, with Josh Matavesi seemingly securing an incredible last-minute victory.
But after the TMO was called for, it was deemed there was a knock-on at the breakdown in the phases beforehand, cruelly denying Ospreys the victory and ending the game in the most pulsating way possible to ensure it is Munster who will play in next week's Pro12 final.
Tries: Zebo, Hurley, Butler
Pens: Keatley 2
Tries: Webb, Hassler
Pens: Biggar 2
Munster: 15 Felix Jones, 14 Keith Earls, 13 Andrew Smith, 12 Denis Hurley (c), 11 Simon Zebo, 10 Ian Keatley, 9 Conor Murray, 8 CJ Stander, 7 Paddy Butler, 6 Peter O'Mahony (c), 5 Paul O'Connell, 4 Donnacha Ryan, 3 Stephen Archer, 2 Eusebio Guinazu, 1 David Kilcoyne.
Replacements: 16 Duncan Casey, 17 John Ryan, 18 BJ Botha, 19 Billy Holland, 20 Jack O'Donoghue, 21 Duncan Williams, 22 JJ Hanrahan, 23 Ronan O'Mahony.
Ospreys: 15 Dan Evans, 14 Jeff Hassler, 13 Ben John, 12 Josh Matavesi, 11 Eli Walker, 10 Dan Biggar, 9 Rhys Webb, 8 Dan Baker, 7 Justin Tipuric, 6 Dan Lydiate, 5 Alun Wyn Jones (c), 4 Tyler Ardron, 3 Dmitri Arhip, 2 Scott Baldwin, 1 Nicky Smith.
Replacements: 16 Sam Parry, 17 Marc Thomas, 18 Aaron Jarvis, 19 Rory Thornton, 20 James King, 21 Tom Habberfield, 22 Sam Davies, 23 Jonathan Spratt.
Referee: Nigel Owens
Assistant Referees: Leighton Hodges, Ian Davies
TMO: Gareth Simmonds