Rhys Webb's breakaway try in the 56th minute was the decisive part of this nail-biting win, as Munster lost a league tie at home for the first time since April 2010.
This top of the table clash was stop-start throughout and the wet conditions made for a tight, forwards-dominated game.
Lively Munster centre Danny Barnes scored the only try of a poor first half early on, the Ospreys hitting back through the boot of Dan Biggar to reduce the arrears to 10-6 by the interval.
Webb's score, which was sparked by Barry Davies' interception, edged the Welsh region in front and a last-minute penalty from Biggar sealed the triumph.
In their first competitive outing at Thomond Park since last season's grand final win, Munster got off the mark after only three minutes' play.
Hanno Dirksen's clearance kick in the 22 was charged down by Barnes who collected the loose ball and touched down to the left of the posts. Ian Keatley swiftly turned it into a seven-pointer.
Ospreys dominated territory in the opening period and had the platform of a strong scrum in which Duncan Jones was able to exert pressure on youngster Stephen Archer.
A scrum penalty saw Biggar split the posts with his first attempt at goal, only for the Munster scrum to earn a penalty in response and Keatley restored the seven-point advantage.
The place-kickers were both denied by the uprights and in the second quarter, the Ospreys were unable to convert their pressure into points.
Joe Bearman was hauled down just short of the try-line, and Biggar was also swallowed up just in front of the Munster posts.
The hosts were living off scraps of possession and both sides struggled to keep hold of the greasy ball, making for an error-strewn encounter.
In the final minute of the half, Archer gave away a scrum penalty and Biggar drilled his kick over from a right-sided position for a four-point difference at half-time.
Referee James Jones reached for his yellow card when Archer collapsed a scrum four minutes into the second half, and Biggar was successful with the resulting penalty from 40 metres to further reduce the gap.
It was advantage Munster when Denis Fogarty rumbled into the visitors' 22 and Ospreys captain Justin Tipuric was promptly yellow carded for hands in the ruck.
However, Keatley's penalty attempt cannoned back off a post and Munster's advances on the Ospreys line - aided by solid scrummaging from replacement BJ Botha - were thwarted.
Just as Munster piled forward five metres out from the whitewash, a loose pass was intercepted by Davies. The full-back set off on a lung-bursting run and despite the presence of Doug Howlett, some neat passing from Davies and Richard Fussell sent the supporting Webb sprinting over in the left corner.
Some niggle crept into proceedings following a clash of heads between Botha and Richard Hibbard, and the former then won a penalty which Keatley converted to make the score 14-13.
Biggar watched a drop goal shot come back off the right-hand post and Davies was wide to the right from further out. Into the dying minutes, Munster got to within metres of the Ospreys line again only to lose the ball at the breakdown and the siege was lifted.
Rubbing salt into the reigning champions' wounds, the Ospreys pack then won a scrum decision from Jones and Biggar added a clinching three points with the last kick of the night.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.