Jackson and Aled Thomas scored early penalties before Irish international Andrew Trimble intercepted Gareth Owen's sloppy pass to register the only try of the night, with Jackson adding the conversion.
Either side of the break Jackson kicked two more penalties but Thomas responded with two of his own to make it 16-9.
Jackson restored Ulster's ten-point lead before half-time replacement Dan Tuohy was sin-binned, but Thomas missed his kick.
The Scarlets failed to capitalise on their man-advantage but Thomas managed to secure a last-gasp losing bonus point.
Ulster were boosted by the return of Johann Muller while Craig Gilroy started fresh from his star performance for Ireland against Argentina.
Thomas missed an ambitious early penalty attempt from 40 yards out before Jackson put one narrowly wide.
But presented with another opportunity after ten minutes Jackson did not make the same mistake and kicked Ulster into the lead from straight in front of the posts.
Thomas made amends for his miss too on 18 minutes with a wonderfully executed kick from the touchline to level things up.
Just before the half-hour mark Ulster stretched their lead when Trimble intercepted Owen's wayward pass to accelerate away from the Scarlets defence and run in under the posts.
Jackson added the extras and kicked another three points after the Scarlets conceded a penalty from their own scrum.
With only two minutes of the second half gone Ulster continued where they left off with Jackson striking another penalty to stretch Ulster's lead to 16-3.
Thomas then shanked another penalty attempt horribly right of the posts but after Darren Cave was penalised for not rolling away he made no mistake, and added his third penalty on 52 minutes from a difficult angle as the Scarlets upped their intensity.
Four minutes later Jackson gave Ulster some breathing space with another penalty before the Scarlets threatened following a good break from Kieran Murphy only for a forward pass to bring an end to the move.
As the Scarlets pressed Tuohy put Ulster further on the back foot when he was sin-binned for not rolling away just past the hour but Thomas blew the chance to reduce the arrears.
Despite their numerical advantage the hosts failed to capitalise, though Thomas ensured the Scarlets did not go empty-handed when he notched a penalty with the last kick of the match to secure the losing bonus point.
|Scarlets Score Card|
|Ulster Rugby Score Card|