And although the Ospreys were much improved in the second-half, Biggar kicking two early penalties before Barry Davies touched down, Priestland and co held there nerve to snap a winless run of three games in all competitions.
The Scarlets hadn't beaten Ospreys since December 27 2007 but after 15 minutes found themselves 6-0 ahead thanks to two Priestland penalties.
It took the visitors until the 28th minute to get on the scoresheet, thanks to a Biggar penalty, but Tommy Bowe wasted a glorious chance to score the first try of the game when he knocked on with the touchline just metres ahead on the right.
Instead that honour went to Scarlets' Thomas who barged his way over following a scrum after two Kahn Fotuali'I kicks were charged down.
Priestland added the extras and kicked another penalty before the interval for a comfortable lead, the Scarlets looking to extend their impressive run against Welsh rivals, having not lost in their last four derby clashes.
The Ospreys on the other hand hadn't won in their last four games against Welsh teams but did their best to turn things around as they came flying out of the blocks in the second-half and reduced the deficit through two Biggar penalties.
And on 55 minutes the Scarlets' lead was reduced to just two points as full-back Davies went over in the right corner, Biggar unable to make the conversion.
On the hour mark Priestland missed an opportunity to extend the lead when he missed a penalty, but made no mistake with his next two efforts to help the majority of the home crowd to relax.
Ospreys replacement fly-half Matthew Morgan missed a kick of his own with eight minutes left that would have made for a tense finish.
And although Priestland missed a last-gasp attempt at the posts, his 17-point haul was instrumental in a first Scarlets win over the Ospreys in nearly four years.
|Scarlets Score Card|
|Rhys M. Thomas||1||5|
|Ospreys Score Card|