Simon Zebo's try proved the difference at Parc y Scarlets as leaders Munster strengthened their Magners League grip.
The game was finely poised 6-6 in the last quarter when Scarlets centre Regan King lost the ball in contact.
Zebo reacted quickest to hack the loose ball downfield and the Munster wing had the pace to beat the covering defence and touch down for the game's only try.
Paul Warwick converted, adding to his two penalties, with Rhys Priestland scoring all the Scarlets' points.
The defeat was hugely damaging to the Scarlets' play-off hopes, leaving them six points adrift of fourth-placed Ospreys who had lost at Newport Gwent Dragons on Friday night.
Munster, meanwhile, have secured a home semi-final at Thomond Park in the Magners League play-offs and will sit top of the Magners League at the end of the regular season.
Both sides had their chances in a frenetic opening, with Wales wing George North knocking-on with the line beckoning while lively opposite number Zebo was hauled down just short after a fine break from inside his own half.
A penalty by fly-half Priestland did give the home side the lead on 18 minutes, but the Scarlets were struggling to get their fluid game going against some aggressive Munster defence.
After winning a penalty at a Scarlets scrum Munster were level through the boot of full-back Warwick just before half-time, and the Australian then added a second following a further home infringement to give his side a 6-3 interval advantage.
Priestland missed with a chance to level matters three minutes after the restart, but in a repeat of the opening minutes of the first half the Scarlets pressed hard.
When the Scarlets pack shoved Munster's eight back at a scrum, Priestland had another shot at the posts and this time was on target to level things again.
The Scarlets were denied a try when Scotland wing Sean Lamont was held up on the line by a fine tackle from number eight Denis Leamy as Munster continued to frustrate the home side.
And the Irish province almost claimed a try of their own, only for wing Danny Barnes to be shoved out in the corner.
They were not to be denied, though, and as the Scarlets looked to run out of defence three tacklers converged on King, forcing the New Zealand centre to lose the ball.
Zebo pounced, hacking through and easily winning the race to the touchdown, with Warwick adding the conversion for Munster to go a score clear.
Priestland had a chance to cut the deficit but was off target again and despite some desperate late efforts from the Scarlets, Munster - as they so often do - were able to hold on for the points.
Scarlets: Stoddart; North, King, Maule, Lamont; Priestland, Knoyle; R Thomas, Rees, I Thomas; Reed, Turnbull; McCusker, Edwards, Lyons.
Replacements: Phillips for Rees (72), R Jones for I Thomas (78), Gardiner for R Thomas (72), Shingler for Turnbull (72), Welch, Davies for Knoyle (72), S Jones for Lamont (63), Williams for Maule (72).
Munster: Warwick; Barnes, Murphy, Mafi, Zebo; Cusack, Stringer; Horan, Sherry, Archer; Ryan, O'Driscoll; O'Donnell, Ronan, Leamy).
Replacements: Fogarty for Sherry (57), Hurley for Horan (67), Hayes for Archer (57), Quinlan for Ronan (60), Butler, Williams for Stringer (72), Tuitupou for Cusack (40), Deasy for J. Murphy (47).
Referee: Alan Lewis (IRFU).