That win ended a four-game losing run in the RaboDirect PRO12 but the Welshmen's only away victory against an Irish province in their last seven visits came against Connacht in Galway in November.
The Scarlets won 17-9 when Ulster visited Parc y Scarlets in round seven this season to end a four game winning sequence by the Ulstermen against the Scarlets.
And Scarlets' only previous victory at Ravenhill in the PRO12 was in September 2008 but Easterby is confident that run can come to an end.
"We're going to Ravenhill under-strength but we have to be confident that we can back up what we did in Treviso last Friday," he said.
"We've put into place some of the stuff we did well out here against them earlier in the season and Friday's game is one that we can go and win.
"There are very few games that we can afford to drop points in. There are 45 points up for grabs and there are sides around us that will win and lose over the next three rounds. We've given ourselves a fighting chance with that victory last weekend.
"There's a way of trying to beat Ulster and there's a way of trying to stop them as well. We need to be as good as we've been when at our best this season to secure a victory."
Easterby has made only two changes to the starting XV that took on Treviso last week; tighthead prop Samson Lee comes into the starting line-up for Jacobie Adriaanse and second row Johan Snyman replaces Richard Kelly while Olly Barkley is set for his debut off the bench.
Fly-half Paddy Jackson, who scored his first senior international try for Ireland against Wales last weekend, returns in one of four changes for Ulster with centre Luke Marshall, second row Iain Henderson and Nick Williams all returning.
Ulster's only defeat in their last ten matches in all tournaments was to Leinster at the RDS in the RaboDirect PRO12 on December 28 and they have lost just once at Ravenhill in the past 12 months: 12-13 to Glasgow in September.
And prop Tom Court, who will join London Irish at the end of the season, is determined to continue Ulster's quest for silverware.
He told the Belfast Telegraph: "I guess the one thing I'm really pushing for and hoping for this year is that I can do as much as I can to make sure that Ulster get over the line and we get some silverware.
"These are matches we need to win and we know we're good enough to do that. But we have to do it when we step out there."
At Ravenhill, 7.05pm. Live on BBC NI/BBC Wales
Referee: Leighton Hodges (WRU, 36th competition game)
Assistant Referees: Gary Conway, G Glennon (both IRFU)
Citing Commissioner: Gordon Black (IRFU)
TMO: Simon McDowell (IRFU)
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