Scarlets led by a point with no time left on the clock but a superb crossfield kick from JJ Hanrahan to Ronan O'Mahony allowed the winger to touch down in the corner.
Referee Nigel Owens went to the TMO and, after an agonising wait, the try was awarded and Munster's eighth win in a row was secured.
The visitors had led 10-9 with Hanrahan kicking three penalties for Munster earlier in the game but two late yellow cards had Scarlets down to 13 and O'Mahony took advantage as Rob Penney's side repeated their heroics from Perpignan the week before.
Munster now lead the RaboDirect PRO12 by six points from Ulster and face Connacht at Thomond Park on Friday, December 27th (ko 7:15pm).
Tickets for that game can be purchased online here.