Andy Fenby and Rhodri Jones crashed over for first-half tries at Parc y Scarlets to hand the hosts a comfortable 14-3 lead at the break.
Stephen Jones continued to keep the scoreboard ticking over before Emyr Phillips and Kieran Murphy secured the bonus-point.
Ethienne Reynecke hit-back for Connacht but it was a mere consolation and Phil John ensured the Scarlets had the final word.
The Scarlets opened the scoring in west Wales after Dan Newton released Fenby following a Liam Davies tap penalty.
Jones converted from the touchline before Miah Nikora opened Connacht’s account.
But prop Jones rumbled over from close-range and fellow Wales squad member and namesake Stephen converted to hand the Scarlets their 14-3 half-time lead.
The fly-half banged over a penalty quickly after the restart and matters were made worse for the visitors when John Muldoon was sent to the sin-bin.
Phillips charged over for the Scarlets’ third on 56 minutes following a neat flick from Jones, who then converted.
The Scarlets bagged the bonus-point shortly after the hour-mark thanks to a barnstorming Murphy break.
Reynecke hit-back for Connacht but veteran prop John had the last laugh and crashed over for a try at the death.
Â
