DTH van der Merwe scored their only try at the Liberty Stadium, while returning prop Rob Evans carried his international form back onto the club stage with a man of the match display.
Now the Scarlets will look to build on that with a clash against their closest Welsh rivals, the Cardiff Blues, who are 13 points back in the table.
Head coach Wayne Pivac said: "One of the things we've talked about is improving on last year's performances. Trying to be the best team in Wales is one of the things the boys want to do and try and make the top four.
"Today was really important to keep both those goals alive with the Blues coming up next week.
"With the games last night it was important that we picked up those four points to stay ahead of the teams chasing. Rather than sit in the bunch we wanted to get the win to give us some breathing space so we're pleased we got the four points.
"Our focus is another derby next week. The Blues are one of the form sides at the moment. They're scoring a lot of tries, playing some good rugby. We're just focused on that game at this stage. If we can get a win there then we'll be in good shape with three to go."
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