The home side crossed through full-back Richard Fussell, hooker Richard Hibbard, and a penalty try, while fly-half Dan Biggar added 15 points with the boot.
Munster had replacement hooker Damien Varley sent off after 73 minutes for lashing out with his boot, but by then the writing was on the wall for the visitors, for whom Ronan O'Gara kicked 12 points, with his replacement Ian Keatley adding three.
Ospreys welcomed back former Wales captain Ryan Jones for his first start of the season, while tight-head prop Adam Jones also made his first appearance of the campaign, albeit from the replacements' bench.
The hosts were buoyed by their derby win at Scarlets last week, but were also conscious that they had lost their opening two home games against Ulster and Glasgow.
Nevertheless, they made a confident start to Saturday's contest, going 13-0 up against the Munstermen, who were forced into an early change when scrum-half Connor Murray was replaced by Peter Stringer due to a head injury.
After Biggar kicked two penalties to put Ospreys ahead, an attempted box kick by Stringer on the 22 was charged down, allowing the Ospreys to move the ball through centre Andrew Bishop for Fussell to go over.
Biggar missed a fourth penalty attempt before the Ospreys defence was called on to hold firm in the face of an improved passage of play by Munster.
O'Gara twice kicked penalties before the break to reduce the deficit to 13-6, and that became 13-9 three minutes after the interval when he added a third.
The Ospreys stopped the rot with a fourth Biggar penalty after Munster flanker Tommy O'Connell was sin-binned.
The strength of the Ospreys pack was shown up when they were given a penalty try from a scrum after 54 minutes. Biggar duly added the extras to take the lead out to 23-9.
O'Gara added a fourth penalty after Munster changed five of their pack, while his replacement Keatley slotted a fifth to cut the deficit to eight points with 14 minutes remaining.
But an incisive attack started by Fussell saw Hibbard go over for the home side's third try to finally take the game away from Munster, whose night night went from bad to worse when Varley was sent off seven minutes from the end.
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