But quick-fire scores from Sam Tuitupou and Barry Murphy, which were supplemented by Paul Warwick's 17-point haul, guided Munster to a narrow win and the reward of a seven-point lead at the summit of the Magners League.
The Scarlets dictated the early exchanges, but Priestland missed two penalty attempts and his half-back partner Martin Roberts was sin-binned for taking out Denis Hurley as the Munster winger chased a kick.
Warwick missed the target with the resulting penalty, leaving Priestland to open the scoring with a 40-metre effort in the 17th minute.
Warwick replied with two penalty successes, the second coming after a powerful burst from flanker Peter O'Mahony.
O'Mahony infringed at a lineout, allowed Priestland kick the Scarlets level, but the game's first try quickly followed - Warwick nipping in under the posts after a James Coughlan-inspired attack.
The conversion followed from the Australian out-half, yet the Scarlets hit back on the stroke of half-time. Priestland made the midfield incision and Edwards was on his shoulder to take the pass and score, with the extras added for a 13-13 interval scoreline.
Priestland knocked over a galvanising penalty as the second half got underway, following O'Mahony's sin-binning for a maul infringement.
Back came Munster though, putting together two slick phases that resulted in tries.
First, Doug Howlett sent Tuitupou powering through tackles from Iestyn Thomas and Ken Owens and the former All Black centre had the pace to make the line from 25 metres out.
Warwick converted and, three minutes later, it was his short pass that invited centre Murphy to burst clear and leave the Scarlets defence flatfooted on an angled run to the posts.
The simple conversion gave Munster a 27-16 lead and a sniff of a bonus point. That fourth try never came and credit to the Scarlets, they hit back with a 10-point burst.
On 58 minutes, Edwards gathered a ruck delivery from Roberts at pace and wrestled free from Niall Ronan and O'Mahony to dive in under the posts. The extras came from Priestland who rewarded his forwards in the 65th minute with another surefooted penalty.
One point in arrears, this game was now finely balanced. The Scarlets struggled for territory but still came closest to scoring late on. Winger Morgan Stoddart was denied a try by Hurley's vital tackle four minutes from the finish, as league leaders Munster held on.
|Munster Rugby Score Card|
|Scarlets Score Card|