The Tigers led at the break thanks to tries from Thomas Waldrom, Andy Forsyth and courtesy of the referee’s whistle.
But Owen Williams kept the scoreboard ticking and the west Wales out-fit pounced for a hat-trick of tries in the final 10 minutes through Gareth Owen, Nic Reynolds and Andy Fenby.
“It has been a long time coming,” said Easterby.
“To be fair to the players and coaches we have stuck at it, we have come under a bit of criticism and some of that has been justified.
“But what was good was that we rewarded the boys and the fans with a performance and hopefully have set a template for the next four or five weeks which are so important to us.
“Owen kept the scoreboard ticking over which was crucial when we got the ascendancy in the second half.
“We really kicked on after half-time and our scrum, line-out and some of our back play was excellent which rewarded us with the scoreline in the end.”
Williams opened the scoring at Parc y Scarlets but the Tigers hit-back as Waldrom rumbled over from a driving lineout.
Williams edged the Scarlets in front with a succession of penalties but the quickfire sin-binnings of Emyr Phillips and Fenby allowed the Tigers back into the game.
The visitors flexed their muscle at the scrum to earn a penalty try and Forsyth grabbed another after Williams’ fifth penalty.
Williams continued to chip away at Leicester’s lead following the break and the Scarlets fought-back as indiscipline crept into the Tigers’ game.
Fenby raced down the touchline for the first of three tries in the closing stages.
Full-back Gareth Owen was next with a sublime inside line to race under the posts before Reynolds collected his own kick to score.
