Head coach Alan Solomons thought Edinburgh were "absolutely outstanding" as they ended Scarlets' 15-month unbeaten home Pro12 record.
"I've got a lot of respect for Scarlets and they have a good home record for a reason," said Solomons following the 26-15 win in Llanelli.
"To come here and win, especially in such an important game, speaks volumes.
"This is a very tight unit that has faced a lot of challenges this season and they have risen to them all."
The victory lifts Edinburgh above Scarlets to seventh - level on points with Connacht - in the table in the battle for one of the six automatic places for the European Champions Cup.
Scotland players Sam Hidalgo-Clyne, David Denton, Greig Tonks, Tim Visser, Hamish Watson and Ben Toolis all returned for the visitors, although hooker Ross Ford, prop Alasdair Dickinson and centre Matt Scott were rested after their Six Nations exploits.
"We gave away a lot of penalties in the first half but we went in ahead at half-time and spoke about sticking to our systems, being more disciplined and more aware at the breakdown," explained Solomons.
"We did all of that really well in the second half.
"It was a big challenge with a lot of experienced boys not playing but the other lads coming in were terrific - Rory Sutherland and Stu McInally had great games and Ben Toolis is playing fantastic rugby."
With four league matches remaining, Edinburgh are involved in a three-way fight for the all-important sixth spot.
"We have some tough games," he said. "But we are still in contention.
"Although they are home matches, Munster and Leinster are top sides, and the Dragons are always a difficult side away, so there is still a long way to go."
Edinburgh now look forward to a European Challenge Cup quarter-final with London Irish.
"It's a big few weeks for the club," said scrum-half Sam Hidalgo-Clyne, who was man-of-the-match against Scarlets.
"If we can get to the semi-finals, that's something very special.
"There's no reason why we can't win that one. We're a really good side.
"It will be tough but if we stick to our game plan and do the simple things well, I'm sure we can do it."