Steve Shingler slotted five penalties before the break in response, but they couldn't complete the turnaround, replacement scrum-half Gareth Davies picking up a second-half red card as his side fell to their first home defeat in the GUINNESS PRO12 since December 2013.
The result ensured Edinburgh leapfrogged their West Walian opponents and moved level on points with sixth-placed Connacht, with Hidalgo-Clyne quick to admit how influential the win could prove come the end of the season.
"We knew that this was a massive game in terms of getting into the top six, so we were never looking very far past this week," the 21-year-old said.
"It is very tough to get points away at the Scarlets, so it is brilliant that we did.
"They put us under a lot of pressure in the second half and pinned us deep in our own territory, so we had to retain the ball in our 22.
"The first half had been really good for us, and we got back into it at the end of the half and that was important.
"It is great to be back here after spending some time with Scotland and putting what I have learned into use, I got to learn a lot from Greig Laidlaw as a scrum-half and that is really helpful."
Follow us on Facebook, join the conversation on Twitter, sign up to our YouTube channel for extensive match highlights and sign up for our newsletter for regular updates on the GUINNESS PRO12
63x46.png){kind=logo}