But Munster full-back Felix Jones fumbled the ball over his own try line and wing Fenby was quick to pounce on it to give the visitors some much-needed breathing space.
This was Scarlets' seventh win in their last nine RaboDirect PRO12 games, but none would have been more celebrated than this one, their first victory over Munster in 16 attempts.
It was Munster who started the game well and looked likely to help themselves to an early score, some desperate defending keeping Jones at bay after six minutes.
Thomas then had the chance to kick Scarlets into the lead with a penalty on ten minutes, but his effort was taken by the wind and went wide of the posts.
Keatley then had the chance to get the first score of the game with a three-pointer of his own on 22 minutes, and the Munster fly-half duly took his chance.
However just before half an hour Thomas made amends for his earlier miss as he booted an easy penalty from in front of the posts to level the score.
The game was then delayed for a lengthy period as Munster's Niall Ronan had to be stretchered off after a knock on the head.
But despite the delay to an injured team-mate it was Munster who ended the first half in ascendy.
Scarlets defended desperately right before the interval and CJ Stander, who replaced the injured Ronan, was adjudged to have been held up by the television match official.
Scarlets survived and had the chance to stretch their lead just three minutes after the restart but Thomas missed his attempt at the posts.
The fly-half then tried his luck with a drop-goal on 54 minutes but that too missed.
But Scarlets did take the lead on 68 minutes as Thomas finally landed his second penalty, his kick going over after striking the left upright.
And just two minutes left Munster full-back Jones spilled the ball twice on his own tryline and opportunist Fenby pounced, Thomas adding the extras for a 13-3 lead.
Thomas then spurned two chances to extend their lead as he was wayward with two more penalties.
But it didn't matter as although JJ Hanrahan added a last-gasp penalty to earn Munster a losing bonus point, Scarlets secured a historic first victory in Cork.
|Munster Rugby Score Card|
|Scarlets Score Card|