Jackson, who was back in action for his club after being dropped from Ireland's bench, touched down twice in the first half and Tommy Bowe and Tom Court also scored tries, while Ruan Pienaar kicked three conversions but then suffered an arm injury which could be a major worry for the Ulstermen.
The result bolstered Ulster's third-place spot in the RaboDirect Pro 12 and they would have been boosted by the return of Stephen Ferris, who made an impressive return following a long lay-off with injury when sprung from the bench on the hour mark for his first appearance since November 2012.
Scarlets, whose points on Friday night came from Gareth Davies' try and Olly Barkley's conversion and two penalties, still have play-off hopes despite the defeat.
Ulster - who beat Newport Gwent Dragons last time out - struck first in the 14th minute when Jackson kicked through and gratefully collected to score after Aled Thomas failed to pick the bounce of the ball.
Pienaar converted and did so three minutes later when, off a lineout, Jackson broke and fed inside for Bowe to touch down under the posts.
Barkley then landed a 31st-minute penalty to get the Scarlets going after Roger Wilson, making his 150th Ulster appearance, was penalised at the breakdown.
But Ulster immediately hit back as this time Bowe created Jackson's second try from a searing break and pass inside against the grain to put the fly-half under the posts.
Pienaar converted and at 21-3 the home side looked comfortable before Scarlets responded when Davies won a kick and chase from the Ulster 22, with Barkley converting.
The score remained 21-10 at half-time after Barkley missed a 40th-minute penalty effort.
The first 10 minutes of the second half saw the Scarlets put some good approach work together only to lose the ball on the line after a half break from Jordan Williams was snuffed out by Robbie Diack.
Ulster survived and broke out to get a 50th-minute penalty chance but Pienaar hit it wide, and he did so again later on from a more difficult angle.
The Scarlets then had their turn, winning a penalty off a scrum, and Barkley made no mistake to close the gap to eight points after 62 minutes - just before Ferris made his long-awaited comeback, having battled with an ankle injury for over a year.
And though the flanker certainly made his presence felt, Ulster were unable to get over the Scarlets line until the last minute when, with tempers flaring, Tom Court barrelled over and was awarded the score by the TMO.
Jackson - kicking in place of the departed Pienaar - failed to convert the valuable bonus-point try.
- Sports & Recreation
- Ruan Pienaar
- Olly Barkley
- Tommy Bowe
- Tom Court