Moore struck out nine and allowed three hits over five shutout innings for his second Triple-A win and the 6,000th in franchise history as the Durham Bulls crushed the Charlotte Knights, 18-3.
MLB.com's No. 3 prospect walked one and threw 61 of 85 pitches for strikes, leaving his third International League start with a 14-run cushion.
"I had a good fastball and good breaking ball tonight," Moore said. "The change seemed to be there when I needed it, and it makes it easy to work when you have that kind of run support. You can challenge guys a little bit more."
Moore (2-0) lowered his Triple-A ERA to 0.50 and has given up only nine hits while striking out 29 over 18 innings. He began the season with Double-A Montgomery, where was 8-3 with a 2.20 ERA. The 22-year-old left-hander ranks second in the Minor Leagues with 160 strikeouts.
"I didn't go into [Triple-A] thinking I was going to struggle, but at the same time I didn't think I didn't need to give my all," he said.
The Bulls played their first game on May 5, 1902, falling to Charlotte, 12-2. Immortalized in the 1988 film "Bull Durham," they joined the International League in 1998 and have been affiliated with the Rays ever since.
"It's awesome," Moore said. "I knew leading up to it that they had only a few games to get there, and they wanted it."
The Florida native admitted that continuing his rapid climb up the Rays' organizational ladder has put the possibility of reaching the Majors this season in the back of his mind.
"The ultimate goal is to get there and stay there and have some impact," Moore said. "But at the same time, I am trying to keep my head on straight and do what I need to do to get ready for that level.
"I need to continue to work on my fastball command, really move the ball in and out and get ahead and stay ahead in the count. Also throwing my breaking ball for a strike and just continuing to develop those three pitches and the command of them."
Big league veteran Dan Johnson homered and drove in four runs for Durham, while while Russ Canzler went 4-for-6 with a homer and three RBIs. Recently demoted Reid Brignac plated three runs and Stephen Vogt collected three doubles and scored three times.