A Sean Lamont try seven minutes into injury time saw the Scarlets seal a dramatic 35-33 bonus-point victory against Connacht at Parc y Scarlets.
But until that moment the Scarlets, who produced a mistake-ridden display, looked as if they might fall to their second Magners League defeat after their 34-28 reversal in Treviso last week.
Connacht, who were indebted to a try hat-trick from Fionn Carr and 18 points from the boot of outside-half Ian Keatley, will have felt hard done by after a committed performance in a closely-fought game which saw the scoreline level on four occasions.
The Scarlets' tries came through Jonathan Davies (two), Regan King and Lamont, with 15 points kicked by Stephen Jones.
Connacht were fresh from their opening-day win over the Dragons, and made the more impressive start with penalties from Ian Keatley on five and 10 minutes putting them 6-0 ahead.
However, despite poor discipline and handling errors, the Scarlets came back into the contest.
Two Stephen Jones penalties were sandwiched by a finely worked try from the home side's first real attack - Jones putting Samoan lock Jonny Fa'amatuainu through a gap before Regan King sent fellow centre Jonathan Davies over.
Connacht did not let their heads drop when the Scarlets went into a 13-6 lead, though, and got back on terms almost immediately.
Full-back Gavin Duffy did well to collect Jones' restart and the ball was moved quickly to left wing Carr, who finished off an impressive team try.
Connacht seemed to start dictating play towards half-time but suffered a blow when their skipper Frank Murphy got himself sin-binned for a high tackle on Scarlets full-back Andy Fenby.
With the extra man the Scarlets scored an injury-time try, Davies collecting a Jones chip and putting King over by the posts.
Connacht were still without Murphy after half-time, but soaked up some early pressure before Carr ran away 60 metres for his second try. Keatley's conversion locked the score at 20-20 on 45 minutes.
The Scarlets had plenty of possession as they attempted to get back into the lead but every attack was littered with poor passes and handling errors.
It took a Connacht transgression for Scarlets to get into the lead when Jones slotted over a 62nd-minute penalty goal.
But Connacht responded with a penalty goal for Keatley three minutes later and then Carr cut inside to complete his treble and put the Irish side 30-23 up.
Connacht suffered a second sin-binning when Ronan Loughney was penalised for kicking a ball out of a ruck, though, enabling the Scarlets to tie the scores at 30-30 when Davies went in for his second try.
The visitors went ahead for only the second time in the contest when Keatley put over his fourth penalty but then, in a frantic finish, the Scarlets eventually got the ball out to Lamont for the winning try to send the home fans into raptures.
Tries: Davies 2, King, Lamont
Con: Jones 3
Pen: Jones 3
Tries: Carr 3
Con: Keatley 3
Pen: Keatley 4
Scarlets: 15 Andy Fenby, 14 George North, 13 Regan King, 12 Jon Davies, 11 Sean Lamont, 10 Stephen Jones, 9 Martin Roberts, 8 Rob McCusker, 7 Johnathan Edwards, 6 Josh Turnbull, 5 Jonny Fa'amatuainu, 4 Lou Reed, 3 Rhys Thomas, 2 Matthew Rees (c), 1 Phil John.
Replacements: 16 Ken Owens, 17 Iestyn Thomas, 18 Peter Edwards, 19 Dominic Day, 20 Nic Cudd, 21 Tavis Knoyle, 22 Gareth Maule, 23 Rhys Priestland.
Connacht: 15 Gavin Duffy, 14 Troy Nathan, 13 Niva Ta'auso, 12 Keith Matthews, 11 Fionn Carr, 10 Ian Keatley, 9 Frank Murphy (capt), 8 Mike McComish, 7 Ray Ofisa, 6 Michael McCarthy, 5 Bernie Upton, 4 Michael Swift, 3 Jamie Hagan, 2 Sean Cronin, 1 Brett Wilkinson.
Replacements: 16 Adrian Flavin, 17 Ronan Loughney, 18 Rob Sweeney, 19 Dave Nolan, 20 Shane Coneely, 21 Cillian Willis, 22 Miah Nikora, 23 Tiernan O'Halloran.
Referee: Neil Paterson (Scotland)
Assistant referees: Tim Hayes (Wales), Wayne Davies (Wales)