Despite Glasgow's impressive start to the new campaign, the Scarlets can take comfort from their last five matches against Scottish opponents. All five have seen victories for the Parc y Scarlets outfit, who have only lost once to the Warriors in their last six meetings.
Easterby said: "What was pleasing last weekend was to see the clarity on how we wanted to play the game coming through in our performance.
"We were probably a little disappointed not to come away with another try but the four points was vital and the way we went about getting the win was impressive after the disappointment of the derby night.
"We had a reaction from the players and we need to build on what we achieved in Edinburgh. Going away and getting a result in this competition is good but we also have to improve our home form. Building home success is crucial for us this season."
Wales centre Jonathan Davies again leads the side with fellow internationals Liam Williams, Rhys Priestland, Ken Owens, Josh Turnbull and Rob McCusker all starting. Rhodri Williams again gets the nod over Aled Davies at scrum half.
On the prospect of facing an inform Warriors side, Easterby added: "Glasgow have been very impressive, they were strong at the end of last season and have kicked off in the same vein.
"They will come down with lots of confidence. If there is any momentum swing away from us, it's important we stick to our principals and keep our heads. We have to show balance and the ability to understand when we can play a certain way and how to manage a game well."
Easterby has given Davies the captaincy for his second game and paid tribute to both the Scarlets centre and co-captain McCusker for their input so far this season.
He said: "Jon and Rob are working well together and it's positive to have the ability to change leadership on the field over a long season of rugby.
"Jon was excellent throughout last weekend in Murrayfield, he has respect and credibility as leader and was full of energy. Rob was able to focus more on his own performance and as a result, he had one of the best games I've seen for a long time in the eight position."