Another Ulster error proved costly as David Lyons broke off the back of a scrum 30m out.
Scarlets took the lead through David Lyons but Sarries hit back as Francisco Leonelli and Noah Cato went over.
David Lyons and then Jonathan Davies went over but a missed conversion left them needing another try to win.
Regan King, Edwards again and David Lyons were also involved in a classic example of fast hands and superb off-loading.
"Our form hasn't been bad in the league but our results have been terrible, " captain David Lyons told BBC Sport.
An early try from David Lyons and Stephen Jones' boot helped the home side to an early 13-0 lead in Llanelli.
Centre Alex Grove has signed a two-year deal and flanker Jake Abbott, lock David Lyons and fly-half George Crook have all penned one-year contracts.
But Owen Finegan (ankle) and David Lyons (thigh) are expected to be fit to face the Irish after sitting out the game against the Pumas.
Rhys Priestland replied with his first opportunity for the Scarlets, who had started to make some inroads into the Blues' half, thanks in no small part to captain David Lyons.
Ian Humphreys put Ulster into the lead with a 12th-minute drop-goal, but a 40-metre charge by home number eight David Lyons failed to produce a response as the move fizzled out.
But instead of using the two-man advantage, Leinster were guilty of their own indiscipline just before the break when prop Stan Wright saw yellow taking David Lyons out at the side of the ruck.
Utilities have historically outperformed in the 15 to 24 months after a recession, explains Hilliard Lyons analyst David Burke.
应用推荐