The Scarlets put themselves back into the Pro12 top four play-off places with this victory over Connacht.
Lock Joe Snyman Number scored the Scarlets only try - his first try for the region - at Parc Y Scarlets.
Young fly-half Owen Williams kicked all 20 points on offer to him, including six penalties and a conversion, to give the Welsh side a vital victory.
South African-born wing Danie Poolman and lock Mike Smith crossed for tries for the Irish province.
The Scarlets, who last lost to Connacht in Wales back in 2004, were desperate to get their Pro12 campaign back in the road.
The Welsh side ended a five game losing run with their 40-19 LV Cup win over Leicester Tigers last Sunday - their first home win since mid-November.
Fly-half Williams, 20, kicked four first-half penalties to give the home side a 12-8 lead at the break after wing Poolman has scored the game's first try in the right corner after he latched on to a cross kick after only 29 seconds for Connacht.
Dan Parks, the former Blues fly-half, who is now a player-coach with Connacht, had a mixed evening with the boot but did land a drop goal for the visitors just before half-time.
Murphy then scored the Scarlets only try after half-time to stretch the Welsh side's lead, but it was fly-half Williams' boot that kept the home side ahead.
Replacement prop Loughney managed a consolation try for Connacht, who had outscored the Welsh side by two tries to one, but only after Williams had provided an impressive 17-point cushion for the Scarlets.
This was Connacht's sixth defeat in all competitions since they beat Zebre 19-10 in Parma in the European Cup on 13 October.
Scarlets: Gareth Owen, Andy Fenby, Nick Reynolds, Adam Warren, Kristian Phillips, Owen Williams, Aled Davies; Phil John, Emyr Phillips, Samson Lee, George Earle, Johan Synman, Rob McCusker (capt), Josh Turnbull, Kieran Murphy
Replacements: Maule for K. Phillips (51), A. Thomas for O. Williams (74), G. Davies for A. Davies (68), Myhill for E. Phillips (74), Manu for Lee (63), Ball for Earle (63), Rawlins for McCusker (74).
Not Used: Hopkins.
Connacht: T O'Halloran; D Poolman, E Griffin, K Tonetti, F Vainikolo; D Parks, K Marmion; B Wilkinson, J Harris-Wright, N White (capt); M Swift, M Kearney; A Browne, J O'Connor, E McKeon.
Replacements: Duffy for Tonetti (61), Nikora for Parks (68), O'Donohoe for Marmion (63), Ah You for Wilkinson (63), Reynecke for Harris-Wright (61), Loughney for White (61), Faloon for O'Connor (55), Muldoon for McKeon (48).
Referee: Matteo Liperini (Italy)
Assistant Referees: James Jones, Alan Jenkins (both WRU)
Citing Commissioner: Denis Jones (WRU)