Captain Jonathan Davies was one of the Scarlets' three try-scorers in an impressive victory over Edinburgh at Murrayfield.
The Wales and British and Irish Lions centre scored his side's third try in their fifth straight win over Scottish opponents.
Wings Nick Reynolds and Jordan Williams scored a try each, with Rhys Priestland kicking seven points with the boot.
Fly-half Harry Leonard scored all of Edinburgh's points.
While this was an important victory for the Scarlets after their shock defeat to the Newport Gwent Dragons in the recent Welsh derby, Edinburgh are still looking for the second win to get them off the bottom of the table.
But the hosts did not look like beating a Scarlets side they have only overcome once in their last six encounters, despite the visitors having three men sent to the sin-bin over the course of 80 minutes.
Leonard and Priestland swapped early penalties in a tentative opening to a game both sides needed to win to restore some much-needed confidence.
Visiting lock Jake Ball was shown a yellow card for persistent fouling midway through the first half and his return brought a concerted attack that resulted in an impressive score.
Fly-half Priestland's long pass to right wing Reynolds saw him hit the ball at real pace and score the Scarlets' first try.
But the half ended with a penalty from Leonard after a Scarlets scrum offence, so the visitors went in at the break leading 10-6.
Two minutes into the second half, home full-back Greig Tonks handed off the Scarlets' Rhodri Williams before sending Jack Cuthbert on a run that ended with a penalty in the visitors' half that Leonard kicked while John Barclay was sent to the sin-bin.
The Scarlets may have been a man down again but soon produced an exciting score after they took advantage of a weak clearance kick by Edinburgh scrum-half Sam Hidalgo-Clyne.
Priestland gathered the ball before releasing left winger Williams, who went on an arcing run to beat three Edinburgh defenders before scoring in the left corner.
The visitors' third try came eight minutes from time when Priestland kicked to the left wing where home winger Lee Jones knocked the ball over his line and centre Davies was on hand to touch down to secure victory.
By this time Edinburgh's prop WP Nel was in the bin and he was joined by Scarlets' replacement full-back Dan Evans in the closing minutes.
Edinburgh: Tonks, Jones, De Luca, Atiga, Cuthbert, Leonard, Hidalgo-Clyne, Dickinson, Ford, Nel, Gilchrist, van der Westhuizen, Basilaia, Grant, Denton.
Replacements: Dominquez for Tonks (74), M. Tait for De Luca (48), Kennedy for Hidalgo-Clyne (53), Blaauw for Dickinson (63), Cox for Gilchrist (49). Not Used: Hilterbrand, Cross, Watson.
Sin Bin: Nel (72)
Scarlets: L. Williams, Reynolds, J. Davies, S. Williams, J. Williams, Priestland, R. Williams, John, E. Phillips, Lee, Ball, Snyman, Turnbull, Barclay, McCusker.
Replacements: Maule for S. Williams (76), A. Thomas for Priestland (77), A. Davies for R. Williams (67), Evans for John (70), Owens for E. Phillips (49), Adriaanse for Lee (49), Earle for Ball (54), Timani for Snyman (63).
Sin Bin: Ball (24), Barclay (43), Evans (79).
Referee: David Wilkinson (IRFU)
Assistant Referees: Peter Allan, Adrian Graves (both SRU)
Citing Commissioner: John Kirk (SRU)