|Scarlets (15) 15|
|Pens: S Shingler 5|
|Edinburgh (17) 26|
|Tries: Burleigh, Denton Cons: Hidalgo-Clyne 2 Pens: Hidalgo-Clyne 4|
Edinburgh took Scarlets' 15-month unbeaten home Pro12 record to boost their 2015-16 European Cup hopes and dent those of the hosts.
Replacement scrum-half Gareth Davies was sent off for a headbutt soon after coming on in the 57th minute.
Sam Hidalgo-Clyne punished the hosts with the penalty that followed.
Phil Burleigh and David Denton went over for Edinburgh and Hidalgo-Clyne kicked 16 points to Steven Shingler's five Scarlets penalties.
Edinburgh rose above Scarlets to seventh in the table in the battle for one of the six automatic Pro12 places for Europe's top flight next season.
The home team were bolstered by the returns of Wales Six Nations squad members Scott Williams, Rob Evans, Ken Owens and Jake Ball to their starting line-up.
A bruised thigh ruled out full-back Liam Williams while Wales reserve half-backs Davies and Rhys Priestland were on the bench.
Edinburgh included Scotland internationals Sam Hidalgo-Clyne, Greig Tonks and Tim Visser while back-row forwards Alasdair Dickinson and Ross Ford were rested following their Six Nations duty.
Shingler kicked the game's first points, but Edinburgh were first into their attacking stride to produce a memorable opening try.
Full-back Jack Cuthbert's offload set up the counter-attack that led to the opening try for Burleigh.
The Edinburgh centre went over after a well-timed one-two with wing Visser.
Hidalgo-Clyne added the conversion only for Shingler to kick four more penalties by the 25th minute.
Edinburgh fly-half Greig Tonks was sin-binned for holding on too long in the tackle to allow Shingler to succeed with the last of those shots.
But half-back partner Hidalgo-Clyne kicked a penalty after Scarlets' Scotland back-rower John Barclay was sin-binned for a similar offence.
And the visitors took the lead at the break after number eight Denton went over and Hidalgo-Clyne converted.
Alan Solomons' side remained in the lead and exerted increasing control as the game wore on.
Scarlets boss Wayne Pivac sent on Davies in a bid to regain the initiative.
But when the twice-capped scrum-half's tussle included a head-butt on centre Andries Strauss, Irish referee John Lacey had no hesitation in banishing the Scarlet.
Hidalgo-Clyne's boot ensured there was no way back for the home side.
Scarlets: Jordan Williams; Harry Robinson, Regan King, Scott Williams, Hadleigh Parkes; Steven Shingler, Aled Davies; Rob Evans, Ken Owens (capt), Peter Edwards, Jake Ball, George Earle, Lewis Rawlins, James Davies, John Barclay.
Replacements: Emyr Phillips, Phil John, Jacobie Adriaanse, Jack Payne, Rory Pitman, Gareth Davies, Rhys Priestland, Michael Tagicakibau.
Edinburgh: Jack Cuthbert; Tom Brown, Phil Burleigh, Andries Strauss, Tim Visser; Greig Tonks, Sam Hidalgo-Clyne; Rory Sutherland, Stuart McInally, WP Nel, Anton Bresler, Ben Toolis, Mike Coman (capt), Hamish Watson, David Denton.
Replacements: Neil Cochrane, Grant Shiells, John Andress, Fraser McKenzie, Roddy Grant, Nathan Fowles, Tom Heathcote, Sam Beard.
Referee: John Lacey (IRFU)
Assistant referees: Chris Williams, Martyn Lewis (both WRU)
Citing commissioner: Ray Wilton (WRU)
TMO: Derek Bevan (WRU)