Connacht meanwhile, paid the price for conceding too many penalties, handing Williams to chance to keep the scoreboard ticking over and guide Scarlets into fourth place and back into the play-offs.
Connacht flew out of the blocks and opened the scoring after just 34 seconds, South African winger Poolman dotting down in the corner for his fourth try of the season.
Fly-half Dan Parks was wayward with the conversion however and four minutes later Scarlets fly-half Williams reduced the deficit with his first penalty of the night.
Parks was handed the chance to respond in kind sooner after but his kick struck the upright and that gave the Scarlets the opportunity to take the lead on 20 minutes.
Williams made no mistake and from there the Scarlets grew into the game, dominating proceedings up front and piling the pressure onto Connacht.
The visitors stood firm however and on 29 minutes, Connacht, after enjoying some territory of their own, moved ahead again when Parks hit the target with a drop goal.
In a topsy turvy first half however, the lead changed hands again as more indiscipline from Connacht handed Williams another shot at three points, one he duly accepted.
And after being pinged for not releasing, after another fine effort from Williams, who missed another kick from out wide and on halfway on the stroke, Connacht found themselves 12-8 down at half-time.
After a flurry of Connacht substitutions after the break, it was the Scarlets who struck the decisive blow on 53 minutes when second row Snyman rounded off some concerted Scarlets pressure by finding the gap to surge over.
Williams continued his fine evening by added the extras to hand Scarlets a 19-8 victory and he further extended his side's lead with his fifth penalty of the night on 63 minutes.
With eight minutes remaining Williams continued his fine night with yet another penalty with Connacht again infringing just in front of their posts.
But back came Connacht in search of a bonus point and that became much more of a possibility when second row Mike Swift made the break and offloaded to replacement front row Ronan Loughney to score.
Another replacement, fly-half Miah Nikora, was on target with the conversion to trim the deficit to ten with four minutes to go but Connacht could not find the further score they needed to gain a losing bonus point.
|Scarlets Score Card|
|Connacht Rugby Score Card|