Paddy Jackson opened the scoring for Mark Anscombe's side after nine minutes when he slotted over a long-range effort from just inside the Scarlets' half.
That penalty was cancelled out ten minutes later when Llanelli fly-half Aled Thomas was successful with a kick from the touch-line.
Then, came the highlight of the half - Ulster Winger Andrew Trimble intercepted a pass from Scarlets' centre Gareth Owen and sprinted half the length of the pitch to score under the posts. Paddy Jackson converted to make it Ulster 10 Scarlets 3.
Paddy Jackson hit another penalty before half time to mean that Ulster went in at the break 16 points to three up.
HALF TIME LLANELLI SCARLETS 3 ULSTER 16
Jackson started the second half where he left off the first, slotting over a penalty to make it Scarlets 3 Ulster 16 and to give the away team a 13 point cushion.
But two penalties in quick succession from Aled Thomas reduced the gap to seven points and it looked like Ulster's winning run could be under threat.
With 20 minutes remaining, Ireland internationals Rory Best and Tom Court came on and won a penalty at their first scrum.
Jackson knocked it over - Scarlets 9 Ulster 19.
Dan Tuohy was sin-binned in the 63rd minute but Scarlets out-half Aled Thomas missed the simple penalty. He made amends in the 80th minute when he got three points with the last kick of the game to secure a losing bonus point for the home team.
The result means Ulster have recorded ten RabboDirect PRO 12 wins in a row, 12 successive victories in all competitions and Mark Anscombe is still yet to lose as Ulster Head Coach. Ulster are now nine points clear at the top of the RaboDirect PRO 12 but they face their sternest test of the season on Friday night when they face Northampton at Franklin's Gardens. A win there and it really could be a season to remember.
|Scarlets Score Card|
|Ulster Rugby Score Card|