Having trailed 8-3 at half-time, converted tries from scrum half Greig Laidlaw (47 minutes) and replacement Craig Hamilton (56) were enough, in the end, to guide Edinburgh to only their second win in five league games.
Speaking afterwards, Edinburgh coach Rob Moffat said: "We won the game and that is what it is all about. I think we played better in the second half than we did in the first half.
"We kicked better in the second half and took our chances. But we know we will need to play better with a big month coming up.
"We've got two European games against Bath followed by back-to-back matches against Glasgow and the players will need to improve for those challenges.
"It was obvious we hadn't played together for a few weeks and we will be targeting improvements."
A losing bonus point was all the Scarlets had to show for their efforts in a game which began positively for them with a third minute penalty from Rhys Priestland.
The Welsh region were without international quartet Matthew Rees, Mark Jones, Dafydd Jones and Morgan Stoddart, but the Test-capped Sean Lamont, Jonathan Davies, Martin Roberts and Deacon Manu all started and player-coach Simon Easterby and captain David Lyons added their experience in the back row.
With Mike Blair and Allister Hogg both out injured, full-back Chris Paterson captained an Edinburgh side that showed five changes to the one which beat the Newport Gwent Dragons last time out, with fly-half David Blair making his first start in almost nine months.
Scotland back rower David Callam also made his long-awaited return from a long term hip injury, coming on in the second half for his first appearance since September 2008.
After a good hit by home prop Iestyn Thomas on Edinburgh flanker Ryan Grant forced a penalty, Priestland stepped up to kick the Scarlets into an early lead.
But man-of-the-match Blair booted the visitors level, four minutes later, with a well-taken drop goal from 35 metres out.
There was a good deal of rustiness on show from both sides and neither could get going in attack on a difficult night for ball-handling.
Priestland missed his second penalty attempt on 21 minutes, but Nigel Davies' men were soon celebrating the game's opening try.
On the half hour mark, the try deadlock was broken by flanker Richie Pugh. Centre Jonathan Davies made a forceful break, doing the initial damage, before Roberts and Lou Reed took the ball on. It was worked out to Andrew Fenby who jinked his way down his wing before passing for the supporting Pugh to round off the score.
Priestland missed the conversion from a difficult angle and watched a penalty effort from a similar position miss the posts as the Scarlets headed for the dressing rooms at half-time with an 8-3 lead.
But, on the resumption, Edinburgh turned up the heat on the hosts. Prop Geoff Cross went close to scoring a try - television match official Nigel Whitehouse ruled it out - before Laidlaw darted through to breach the Scarlets whitewash, with Paterson's successful conversion putting the Scots in front for the first time.
Wales and Lions ace Stephen Jones was then introduced at fly-half by the Scarlets, Davies moving Priestland to full-back as Daniel Evans departed.
And Jones was involved in the score which saw the home side edge ahead again on 52 minutes.
His half-back partner Roberts set the wheels in motion with a fine break from a ruck in the visitors' 22, Edinburgh held out until some good continuity led to Jones sending winger Lee Williams over for an unconverted try.
The ebb and flow continued as Edinburgh responded with another seven-pointer. Impressive Blair did well to escape Lyons' clutches before passing for replacement lock Craig Hamilton to thunder over for a timely Edinburgh try, which Paterson converted for 17-13.
The Scarlets' hopes were hit when replacement flanker Josh Turnbull caught Edinburgh's Nick de Luca with a dangerous tackle which resulted in Turnbull receiving a yellow card from Italian referee Carlo Damasco.
Before Jones closed the gap to three points with a 69th minute penalty, young centre Davies missed out on a glorious chance to convert a three-on-one overlap and the Welshmen were left to count the cost of those missed chances as Edinburgh controlled the closing stages and dominated territorially to see out a hard-fought win.
|Scarlets Score Card|
|Edinburgh Rugby Score Card|