Edinburgh held on to overcome Scarlets in an exciting encounter at Murrayfield and take vital Magners League points.
Rhys Priestland's penalty gave Scarlets an early lead, but the boot of Phil Godman and a Roddy Grant try put Edinburgh in control.
Phil John's try reduced the deficit, but Tim Visser replied for Edinburgh after the break.
Godman's boot appeared to put Edinburgh out of reach until Andy Fenby's try led to a nervous finish.
It was a mixed performance in Edinburgh's quest for a top-four finish and missing out on a bonus point, combined with Munster's 27-19 win over Glasgow, meant that Rob Moffat's side drop to third.
Unlike many Welsh teams that venture to Scotland, the Scarlets were quickly out of their trap, forcing a five-metre line-out followed by a scrum.
Godman kept the scoreboard turning over for Edinburgh
When a ruck developed under the Edinburgh posts, home number eight Grant tried to kick the ball free and the deserved penalty was slipped home by Priestland in the fourth minute.
Late injury call-offs by Edinburgh centres Nick De Luca and Ben Cairns had produced a very different back line from the one originally chosen, with international centre Simon Webster given his second start of the season.
He was prominent in the 12th minute, released after good work by Mark Robertson.
The ball got into the visitors' 22 and, when they went offside, Godman kicked the simple penalty to tie the score.
Edinburgh attacked down the other wing, with Visser and Ross Rennie prominent, producing another penalty that was slotted home to give Edinburgh the lead after 14 minutes.
With both backs and forwards offloading, Edinburgh then enjoyed a good spell crowned by a magnificent try by Grant in the 27th minute.
Following a Robertson up-and-under plus chase, the ball was fed to the number eight well outside the Scarlets 22, but he found a way through the traffic and then accelerated to score under the bar with Godman converting.
Instead of pulling away, Edinburgh found themselves under the cosh.
Scarlets left winger Fenby shot up his wing and, when the ball came inside, crisp handling involved Priestland, David Lyons and Phil John, with the latter touching down and Priestland converting.
Errors by Robertson and Jim Thompson allowed the visitors to stay on the attack, but Edinburgh were able to go in leading 13-10.
Edinburgh's restart saw an immediate try. Mike Blair broke clear on halfway and kicked left, where the ball broke to Visser, who scored, although Godman could not convert.
Priestland and Godman then exchanged penalties before Edinburgh got a lucky break when Scarlets replacement hooker Matt Rees charged down and secured Blair's clearing kick but put a foot in touch to deny him a score from seven metres.
A drop goal from Godman after 60 minutes seemed to have eased Edinburgh away, but a try from Fenby that started innocuously but left numerous Edinburgh players looking at one another, converted by Dan Newton, narrowed the home lead to 24-20 and a nervous last 10 minutes ensued.
Edinburgh coach Rob Moffat: "It could have been better, but at least we got the win.
"I thought we were very sloppy and made far too many individual errors.
"With the amount of ball we had, we should have scored four tries and won a bonus point.
"We obviously have to win all our games now as it's very tight at the top, even in points difference, so every point is very important."
Scarlets hooker Matthew Rees
: "We knew it was going to be a difficult challenge coming to Murrayfield.
"What killed us was that try just after half-time. From then on, we were just chasing the game.
"This season has been frustrating to say the least. We targeted this game and we just need to go back and prepare for the big one against the Ospreys next week."
Edinburgh: Robertson, Webster, Thompson, Houston, Visser, Godman, M. Blair, Traynor, Kelly, G. Cross, MacLeod, S. Turnbull, MacDonald, Rennie, R. Grant. Replacements: D. Blair for Godman (64), Laidlaw for M. Blair (64), Jacobsen for Traynor (54), Ford for Kelly (54), MacKenzie for S. Turnbull (67), Newlands for MacDonald (66). Not Used: Brown.
Scarlets: Evans, L. Williams, King, J. Davies, Fenby, Priestland, Roberts, John, Owens, R. Thomas, Welch, Day, Turnbull, Pugh, Lyons. Replacements: Maule for L. Williams (66), Newton for Priestland (53), Knoyle for Roberts (60), Rees for Owens (37), Manu for R. Thomas (54), Reed for Day (54), McCusker for Pugh (60).
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