Andy Fenby, Kieran Murphy, Emyr Phillips, Rhodri Jones and Phil John added to the scoreline with a try each to equal the club's best run for six years.
Tiernan O'Halloran almost handed Connacht the perfect start only to be denied by desperate Scarlets defence in the fourth minute.
There was little between the sides in the opening exchanges but Scarlets finally got themselves on the board on 16 minutes.
After electing for a five metre scrum rather than a simple shot at goal, the ball was eventually swept wide and Fenby scampered over.
Stephen Jones converted the extras but Connacht responded with sustained pressure in the Scarlets half and eventually reduced the deficit when ex-Hurricanes fly-half Miah Nikora slotted a 24th minute penalty.
Connacht consistently failed to capitalise on the pressure they had built and were punished when Scarlets struck again three minutes before the break.
Camped on the Connacht line it was left to Rhodri Jones to execute the pick and drive with Stephen Jones once again successful with the conversion.
Stephen Jones began the second half as he ended the first, adding a further three points before Scarlets crossed again when Phillips capitalised on John Muldoon's yellow card and piled over under the posts for a converted try.
Connacht attempted to drive themselves back into contention but the Scarlets defence was just too strong and the Welsh side secured themselves a bonus point just after the hour mark.
Still down to 14 men Connacht were powerless to prevent the Scarlets claiming a bonus-point score when Murphy went over and Stephen Jones again added the extras.
When Scarlets lost Peter Edwards to the sin bin it was the Irish side's turn to take advantage, with Ethienne Reynecke the man to cross the whitewash.
Undeterred Scarlets continued to press for a further score and with the final move of the game Matt Gilbert and Dan Newtown combined to send prop Phil Jones over.
Stephen Jones celebrated being named man of the match to kick the final points and round off a comfortable victory for the Scarlets.
|Scarlets Score Card|
|Connacht Rugby Score Card|