The Scarlets won for the first time in five visits to Ireland, holding off Connacht's frantic finish to triumph 24-21 in Saturday's RaboDirect PRO12 clash at the Sportsground.
Having trailed 24-9, Pat Lam's men produced a late spurt as full-back Gareth Owen became the third Scarlets player to be yellow-carded during this exciting encounter.
But Connacht were unable to conjure up a match-winning score and their seventh defeat saw them remain rooted to the bottom of the table.
Winger Frazier Climo scored a try on his league debut to edge the Scarlets 10-9 ahead at half-time after Connacht fly-half Craig Ronaldson had converted three penalties.
Further tries from Jacobie Adriaanse and Gareth Davies strengthened the Llanelli side's hand and, although Matt Healy and Jason Harris-Wright touched down for Connacht, the visitors deservedly took the spoils.
Connacht were rewarded for their early endeavour when Ronaldson knocked over his first two shots at the posts, with Jake Heenan and Kieran Marmion both prominent.
The Scarlets - hampered by international call-ups as well as a series of handling errors - improved as the first half wore on and Aled Thomas punished Connacht captain Craig Clarke for not rolling away in the 21st minute.
But Simon Easterby's charges were under intense pressure after Heenan and Marmion played their part in an attack that almost led to a try for debutant number eight Eoghan Masterson.
Cynical play close to the Scarlets line led to prop Adriaanse being sin-binned, however the Connacht try that looked so likely during this period never came.
A third Ronaldson penalty was their only reward and the Scarlets stung them with a late try before the break.
Gareth Davies did well to create the opportunity with a dummy pass, allowing newcomer Climo to pick a good line and finish in comfortable fashion to the left of the posts.
Thomas' conversion moved the visitors ahead for the first time, and referee Matteo Liperini angered Connacht when he blew for half-time while they seemingly had a penalty advantage.
Their frustration grew when the Scarlets pack rumbled over from a lineout maul with prop Adriaanse getting the touchdown. The try came after Ronaldson missed touch from a penalty and was off target from a 40-metre penalty.
Thomas added the extras to the visitors' second try and he turned their third into a seven-pointer too, the well-drilled Scarlets upping the ante with Davies sniping through for a deserved score from close range.
Connacht, now 15 points adrift, got a lifeline when Healy scooped up a loose pass and sprinted clear to run in an intercept score which Ronaldson converted.
The Scarlets stuttered again when Aaron Shingler was yellow-carded for pulling back Heenan and replacement Dan Parks booted the penalty to touch, setting up a well-constructed drive that led to hooker Harris-Wright crashing over.
Unfortunately for the home fans, Parks missed the kick to make it a one-point game and the Scarlets' stubborn grip on the match points could not be relinquished.
In a breathless finish, Connacht failed to profit from a brilliant 60-metre break from replacement Fionn Carr and the ball then beat Climo into touch as he hunted for his second try.
Lam's side exerted more pressure in the dying minutes, after full-back Owen was sin-binned for a late tackle on Healy, but the Welsh side managed to keep them out.