The try that sealed the victory didn't arrive until the 74th minute at which point the outcome was still very much in the balance with Munster leading by just four points (17-13) and playing with 14, Marcus Horan, having been yellow carded.
Jerry Flannery made the initial surge and when the ball was spun wide, Shaun Payne came into the line to create the space to put Carney over in the corner.
The Scarlets won the toss and opted to play into the strong wind. They went behind when Flannery scored after just six minutes but responded in the best possible fashion with a try five minutes later from Stephen Jones whose conversion edged the visitors in front.
O'Gara added three penalties and Munster went in at the break leading 14-7.
Jones kicked a 49th minute penalty and in a two minute period at the start of the final quarter, swopped penalties with O'Gara to leave just four points separating the sides.
With Horan cooling his heels in the 'bin' the Munster pack once again rolled up their sleeves and provided the opening for Carney's try.
Munster: S Payne; B Carney, R Tipoki, L Mafi, I Dowling; R O'Gara capt, P Stringer; F Pucciariello (M Horan 51 min)), J Flannery, J Hayes; D O'Callaghan, M O'Driscoll (D Ryan 63 min)); D Leamy, D Wallace, A Foley (F Pucciariello temp).
Llanelli Scarlets: M Stoddart; M Jones, R King, J Davies, N Brew; S Jones, D Peel; I Thomas, J Hayter, B Broster; V Cooper, A Eustace; S Easterby capt, J Bater, A Popham.
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