Ireland player Simon Easterby scored a try for Scarlets
Connacht (8) 15
Tries: Mostyn, McHugh
Scarlets (20) 37
Tries: Daniel, Easterby, King (2)
Cons: Jones (4)
Pens: Jones (3)
The Scarlets ended Connacht's unbeaten start to the season as they won for the third time in seven days.
The Welsh side also scored four tries to take a vital bonus point in Galway.
Tries from Darren Daniel, Simon Easterby and a second-half brace from Regan King were decisive, while Stephen Jones kicked a total of 17 points.
Stand-in Connacht captain Mark McHugh tallied 10 points with a converted try and a penalty while Matt Mostyn scored a first-half touchdown.
Jones opened the scoring with a third-minute penalty but moments later McHugh and Conor McPhillips combined to put former Newport winger Mostyn in for a try.
After 10 minutes Daniel finished off a flowing move in the corner and Jones converted as the visitors started to take control with open, expansive play.
After a Jones penalty, Scarlets captain Easterby, the Ireland flanker, barged over in the 40th minute for only his second try in Magners League history.
Jones' conversion was followed by an injury-time McHugh penalty, which left Connacht trailing by 20-8 at the break.
Jones knocked over an early penalty after the break but McHugh responded with a breakaway try after an uncharacteristic loose pass by Jones.
Replacement centre King, barely on the field, soon tore in under the posts for Jones to convert for a 30-15 lead and the classy Kiwi grabbed what could prove to be a vital bonus point when he was put away by Dwayne Peel in the dying minutes.
Connacht: M Mostyn; C McPhillips, P Warwick, G Williams, K Matthews; M McHugh, C Keane; B Wilkinson, A Flavin, S Knoop, D Gannon, A Farley, J Muldoon, M Lacey, C Rigney.
Replacements: J Fogarty, M Diffley, M Swift, B O'Connor, T Tierney, John Hearty, D Riordan.
Scarlets: Ceiron Thomas; Dafydd James, Matthew Watkins, Gavin Evans, Darren Daniel; Stephen Jones, Clive Stuart-Smith; Phil John, Matthew Rees, Deacon Manu, Adam Jones, Scott Macleod, James Bater, Simon Easterby (capt), Nathan Thomas.
Replacements: Iestyn Thomas, Ken Owens, Inoke Afeaki, Alix Popham, Dwayne Peel, Mark Jones, Regan King.