International star Chris Paterson stole the show for the visitors as they notched their first ever win at Stradey park.
Paterson racked up a total of 16 points thanks to a try in the opening period and 11 points from his boot.
As the first half came to a close it looked as if the relatively inexperienced Scarlets would get their season off to a winning start.
They held a 10-3 advantage before the break but had no answer to a brave comeback from the Gunners.
Paterson put his side ahead with a penalty after quarter of an hour but Llanelli fullback Barry Davies skipped over for a try and former Sale flyhalf Mike Hercus put the home side in control.
But Edinburgh rallied before the break with Paterson going over in the corner.
The Scot added another penalty early in the second half to give his side the lead once more and scrum-half Mike Blair grabbed their second try on the hour mark.
The conversion and a later penalty from Paterson looked to have put the game out of reach for the Scarlets but they responded with another try from Barry Davies ensured a tension-filled finale.