The fly-half was wayward with just one of his six kicks, while wing Andrew Trimble claimed the only try of the game as he ran 70 metres after an interception.
The Scarlets did at least manage an injury-time losing bonus point as number 10 Aled Thomas kicked his fourth penalty.
Minus all their Wales players the Scarlets made a late change with Nic Reynolds replacing the injured Gareth Maule in the centre.
Ulster made nine changes in a team featuring captain Johann Muller.
The match was far from a classic — the wet conditions making life tough and both outside-halves, Thomas and Jackson, missed early penalty attempts.
But on 10 minutes the Scarlets were caught offside from a kick and Jackson broke the deadlock with a penalty.
The Scarlets became the first side to put together some phases although it ended with Ulster scoring the first try of the game.
Centre Gareth Owen’s pass was picked off by Trimble, who raced in from 70 metres to score. Jackson converted to give Ulster a 10-3 lead on 28 minutes.
And there was more trouble for the Scarlets as they were penalised at a scrum right in front of the posts on their 22. Jackson made no mistake with the penalty kick to open up a 10-point lead by the interval.
And three minutes into the second half they extended their lead with a third penalty for Jackson. It was an especially crucial kick as Thomas badly missed a penalty attempt just later.
But he did make up for the miss by finding the target twice with penalties on 49 and 53 minutes to cut the visitors’ lead to seven points.
However, the introduction of front rowers Rory Best and Tom Court turned the initiative back in Ulster’s favour as they earned a penalty from a strong scrum, with Jackson converting to restore a 10-point advantage.
Ulster then had replacement lock Dan Touhy sin-binned for a ruck offence and though Thomas was wide with the subsequent penalty, he did land a bonus-point kick late on.
Scarlets scorers: Pens: A. Thomas 4.
Ulster scorers: Try: Trimble. Cons: Jackson. Pens: Jackson 4.
SCARLETS: Newton, K. Phillips, Reynolds, Owen, Fenby, A. Thomas, G. Davies, John, E. Phillips, Adriaanse, Snyman, Kelly, Earle, J. Edwards, Murphy.
Replacements: Warren for K. Phillips (73), A. Davies for G. Davies (52), Hopkins for John (63), Myhill for E. Phillips (18), Manu for Adriaanse (63), Vallejos for Snyman (62).
ULSTER: Nelson, Trimble, Cave, L. Marshall, Gilroy, Jackson, P. Marshall, Black, Herring, Afoa, Muller, McComb, Henderson, Diack, Wilson.
Replacements: Bowe for Gilroy (41), Court for Black (57), Best for Herring (57), Tuohy for Muller (41), McComish for McComb (61).
Referee: Peter Fitzgibbon (Ireland).