The result, Ulster's 12th victory in 13 league games, means they now head into two weeks of European action - where they are Pool Four leaders - in good shape.
However, the Scarlets have now fallen to their fifth defeat in six games - and that run looks likely to worsen as the bottom side in Pool Five fulfil their European pool fixtures over the next fortnight.
Ulster scored five tries - all in the second half - from Robbie Diack, Andrew Trimble, Nick Williams, Neil McComb and a penalty try. Ruan Pienaar kicked all four conversions and two penalties on his 50th appearance.
The Scarlets at least did not endure a repeat of having two players shown red - as was the case against Ospreys on Boxing Day - but they will be bitterly disappointed at this showing which saw Aled Thomas again yellow carded late on.
Leinster stepped up their bid for a play-off spot with an impressive 31-16 bonus point win over a battling, but disjointed, Edinburgh side at Murrayfield.
The European champions had a penalty try as well as touchdowns from Gordon D'Arcy, Jonny Sexton and Ian Madigan, plus 11 points from Sexton's reliable boot.
The hosts, for whom this was a fourth successive defeat in all competitions, had two penalties by Greig Laidlaw and a drop goal from Piers Francis, who added the conversion of a late try for prop Willem Nel.
Fly-half Dan Biggar scored all Ospreys' points as the Welsh side escaped with a narrow 16-15 RaboDirect Pro12 victory after being given a scare by rock-bottom Zebre who out-scored them two tries to one at the Liberty Stadium.
The Ospreys had probably targeted a bonus point win against the winless Italians but an error-strewn display saw them trail until the 66th minute, with a shock Italian win on the cards before that.
Biggar scored three penalties and converted his own try while Zebre scored tries through scrum-half Alberto Chillon and his replacement Tito Tebaldi with Daniel Halangahu converting one and Chillon kicking over a penalty.
Glasgow secured a 41-7 bonus point victory over Benetton Treviso at Scotstoun to stay in contention for a play-off spot.
Treviso were reduced to 14 men in the early stages, allowing Glasgow to dominate - scoring three tries in the first period and two in the second through DTH van der Merwe, Stuart Hogg (2), Tommy Seymour, and Nikola Matawalu.
Ruaridh Jackson proved reliable from the kicking tee, slotting five kicks between the sticks and collecting the man of the match award. Duncan Weir also added to the scoring with two late conversions.
Francesco Minto touched down for Treviso's only try in the second half with Kris Burton on target with the conversion.