Niall O'Connor landed the match-winning kick for Connacht as they came from behind to beat the Scarlets in Galway.
The former Ulster fly-half, on as a replacement for Matthew Jarvis, coolly slotted a 69th-minute penalty and the hosts held on.
The Scarlets led 6-3 at the break and Aaron Shingler's 47th-minute try stretched their lead to 11-3.
But Connacht finished the stronger thanks to a converted try from Mark McCrea and O'Connor's clinching score.
Dan Newton landed his first penalty after John Muldoon was guilty of not rolling away in the ninth minute.
Good work from the industrious Josh Turnbull led to a penalty which Newton turned into three points, but Connacht raised the tempo coming up to half-time.
The Llanelli side were penalised for crossing and Jarvis opened Connacht's account.
Nigel Davies' men seized back control on the resumption though.
After Ben Morgan broke from a close range scrum, a ruck was set up and passes between scrum-half Ruki Tipuna, Emyr Phillips and Iestyn Thomas put Shingler over in the left corner.
Newton could not add the extras and tempers flared a couple of minutes later when Michael Swift and Rob McCusker threw punches at each other, leading to a double sin-binning.
Connacht's try came when Samoan Henry Fa'afili tied in a couple of defenders on a surge up the right and passed one-handed for former Ulster winger McCrea, who picked a lovely angle, to glide over to the right of the posts.
Jarvis converted to put just a point between the sides.
Territorially, Connacht were now on top and a ruck offence allowed O'Connor to kick them ahead for the first and final time.
Connacht: Duffy, McCrea, Griffin, Fa'afili, O'Halloran, Jarvis, F Murphy, Loughney, Flavin, Ah You, Swift, McCarthy, Muldoon, Ofisa, Naoupu.
Replacements: Reynecke, Wilkinson, Maguire, Anderson, J O'Connor, O'Donohoe, N O'Connor, Tuohy.
Scarlets: Evans, L Williams, Gomer-Davies, Maule, L Williams, Newton, Tipuna, I Thomas, Phillips, R. Thomas, Shingler, Day, McCusker, Turnbull, Morgan.
Replacements: Myhill, John, Gardner, Reed, J Edwards, R Williams, A Thomas, Warren.