Scarlets hadn't tasted defeat at home since December 2013 but a perfect display with the boot from Sam Hidalgo-Clyne and tries from Phil Burleigh and David Denton put an end to that.
With back-to-back home games against Munster and Zebre to come in April, Edinburgh sit just outside the top six and level on points with Pat Lam's Connacht.
And Solomons believes it was a performance that says a lot about the mental strength of his team.
"I've got a lot of respect for Scarlets and they have a good home record for a reason," he said.
"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.
"We have some tough games, 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."
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