Liam Williams' try double secured a 17-8 win for Scarlets as they earned a first Guinness PRO12 win of the season and condemned champions Connacht to 12th place.
Niyi Adeolokun's first-half score had cancelled out Williams' first converted try, before Jack Carty's penalty gave Connacht a one-point half-time advantage.
But Wayne Pivac's side looked a different animal after the second-half, piling the pressure on a resilient Connacht side who eventually crumpled when Williams grabbed his second before Rhys Patchell turned the screw with a drop goal.
Pat Lam's side remain winless and welcome Edinburgh to the Sportsground next weekend while Scarlets travel to Italy to take on Benetton Treviso.
The two sides were inseparable for 20 minutes in a scrappy first-half, but it was one of the stars of Connacht's title charge last year - Adeolokun - who broke the deadlock.
Connacht's pack had been gradually getting the upper-hand and a strong scrum put Lam's men in position, before slick hands from prop Denis Buckley sent Adeolokun haring over.
Carty missed the conversion and was off target again, before Scarlets fought back through Williams.
The initial impetus came from Aaron Shingler, the flanker collecting a wide pass and bursting through the Connacht defence.
When the ball was recycled, slick hands between brothers James and Jonathan Davies sent Williams over under the posts, which Patchell converted.
Scarlets were growing into the game, but Connacht were at their dogged best, captain John Muldoon intervened critically on 53 minutes with a goal-line turnover that relived vast amounts of pressure.
Ken Owens' break looked potentially game-breaking and when the ball found Williams on the flank, one outcome looked likely, but he was denied by a stunning Tiernan O'Halloran cover-tackle.
Yet Pivac's men continued to pile forward and despite heroic defence, the men from Galway could not escape their tryline.
Williams then made amends for missing out, with a textbook finish on 66 minutes on the touchline and Patchell found his kicking boots to convert superbly, taking the hosts 14-8 ahead with less than 15 minutes remaining.
An ever-more influential Patchell then thumped over a drop-goal to move Scarlets beyond a converted score.
|Scarlets Score Card|
|Connacht Rugby Score Card|