Aled Thomas and his replacement Owen Williams were wasteful with the boot in the second-half, spurning an avalanche of three-pointers as Edinburgh bravely hung to a narrow lead.
However, in the final quarter, after missing his first three attempts at goal, Owen Williams redeemed himself with a simple penalty in front of the posts to give the Scarlets the narrowest of wins.
Scarlets dominated possession and territory in the opening ten minutes, with Edinburgh, who are on a disastrous run of ten consecutive defeats in all competitions, unable to get their hands on the ball.
Easterby's men were eventually rewarded for their early dominance as Thomas struck the first points of the game with a penalty after the Scottish side were penalised for offside inside their own 22.
Scarlets didn't have to wait long for their first try of the evening as wing Fenby broke a tackle in midfield to score his eighth touchdown of the season in the corner on 14 minutes after a lovely offload by Thomas.
Unfortunately the No.10 was unable to replicate his earlier effort with the boot as he missed the subsequent conversion.
For all of their early dominance, a mistake from Thomas off the restart saw Edinburgh build pressure and with their first visit into the Scarlets 22, Edinburgh No.8 Dave Denton was held up on the line.
Edinburgh continued to press and Liam Williams was penalised for not rolling away, allowing Harry Leonard a simple penalty to get the Scottish outfit on the scoreboard.
Williams was again at fault on 23 minutes as he came charging out of the line, giving space for Leonard to pick out Fife out wide to touch down for a score, with the Edinburgh No.10 adding the conversion to make the game 10-8.
After their early domination, Scarlets seemed to implode as another error at the breakdown gave Leonard a shot at goal but this time the No.10 was left frustrated as his kick fell short.
Scarlets suffered a disastrous start to the second-half as replacement scrum half Gareth Davies saw his kick charged down by Edinburgh's Richie Rees in his own 22, forcing the home side into a mistake in front of their posts, which Leonard punished with a penalty.
Ten minutes after the break Denton was penalised for offside, allowing Thomas a simple penalty kick to drag Scarlets back into the game after a period of sustained pressure from the home side.
After replacing Thomas, Owen Williams missed with his first shot at goal, the ball struck the woodwork from distance after Leonard was penalised at the breakdown.
And the Scarlets were again frustrated minutes later as Jonathan Edwards was held up over the try line at the behest of the television match official.
Denton was again penalised on 59 minutes for not rolling away at the tackle, giving Owen Williams a shot at goal but again the replacement failed to add the three points.
Edinburgh didn't learn from their indiscipline at the breakdown and after persistent offending as team; wing Fife was the unfortunate recipient of a yellow card but again Owen Williams missed his shot at goal.
At the fourth time of asking Owen Williams eventually managed to land three points from in front of the Edinburgh posts to nudge the home side 14-13 in front with just 13 minutes to play.
Scarlets again dominated the final ten minutes but they were unable to turn their dominance into points as Edinburgh held firm.
|Scarlets Score Card|
|Edinburgh Rugby Score Card|