Rhys Priestland also kicked a penalty and two conversions in the convincing triumph for the Welsh side.
However, the result means that Edinburgh are still scratching around for the second win they need to leave the bottom of the table. Their points came from three penalties from stand-off Harry Leonard.
A tentative opening was to be expected from two teams still looking for some good form and it was not relieved until the 15th minute.
Edinburgh gave away a penalty in front of their posts and from it, Jordan Williams came off his wing and was sent close to the line where the move ended when lock Jake Ball was penalised for hanging on.
The same man was again culpable a few minutes later, diving into a ruck set up after a scything run by Priestland.
Scarlets had upped the pace with a policy of kicking into Edinburgh territory and then staying there - until the 24th minute.
Ball was again penalised at the breakdown and found himself sent to the sin bin by referee Davie Wilkinson.
Edinburgh responded with their first sustained spell of possession. Ross Ford and Willem Nel were prominent in taking the ball forward and when Scarlets were penalised on their 22-metre line, Leonard kicked home the simple penalty.
Edinburgh were, however, only ahead for three minutes. They were penalised for not releasing and Priestland scored from wide left.
The return of Ball brought a concerted attack, finishing with a textbook try.
Following a number of territory-securing carries by forwards, Priestland threw a pass out to the right wing for Reynolds, who arrived at pace for the touchdown that the former converted from far out.
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.
Only two minutes into the second half, home full back Greig Tonks handed off 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.
Scarlets were a man down but soon produced an exciting score.
Edinburgh scrum-half Sam Hidalgo-Clyne's weak clearing kick to the visitors' right was fielded by Priestland, who found left winger Jordan Williams. His arcing run bamboozled three Edinburgh men and ended with a try in the left corner.
Scarlets' third try came eight minutes from time with Edinburgh's prop Nel in the bin.
Priestland kicked to the left wing where home winger Lee Jones knocked the ball over his line. The following-up Jordan Williams was there to touch down with Priestland converting from touch.
- Sports & Recreation
- Rhys Priestland
- Harry Leonard