In a thrilling contest at Rodney Parade, Scarlets enjoyed a significant advantage in the scrums and had Dan Jones produce a fine display at five-eighth, but it was not all plain-sailing for the visitors.
Scarlets held a slender four-point advantage at the break, with Samson Lee, Steff Evans and Jamie Davies touching down, while Jared Rosser and Taine Basham scored at the other end.
But Scarlets charged ahead after the interval, with Johnny McNicholl, Tom Rogers and Dane Blacker getting in on the act, while Jones's kicks were on the money five times.
The six-try victory secured Scarlets a bonus point, which moves them second in Conference B, but they need Connacht to do them a favour against Munster on Monday (AEST) otherwise their season will be over.
In Conference A, Leinster and Ulster have already made sure of their places in the play-offs, but the latter will be concerned about its chances in the next stage after disappointing in the two teams' meeting on Sunday (AEST).
Leinster, which gave many fringe players the opportunity to impress, claimed a brilliant 28-10 win at Aviva Stadium.
Ed Byrne's early try sent it on its way, with the boot of Ross Byrne giving them a 13-0 lead at half-time.
Ulster was a little more threatening in the second 40, with Rob Herring getting it back in contention by finishing in the 53rd minute, but Scott Penny and Harry Byrne went over late on to wrap up a superb victory.