The Brazilian right-hander entered Sunday's game with a 2.75 ERA, but without a record over four starts with Winston-Salem.
His season-high nine-strikeout, one-hit outing over seven innings still didn't net him his first Carolina League win. He allowed a run and walked two in his longest outing of the year, but the Dash fell, 4-2, to the Wilmington Blue Rocks.
"I have been pitching well, but it's more important to me that the team does well," Rienzo said. "When the team wins, I'll start getting my wins. If I help the team, I help myself."
Rienzo carried a perfect game into the fifth, and set down the first two batters in that inning without incident. He hit the third, Alex McClure, and then saw his no-hitter come to an end when Carlo Testa followed with a double to left field.
McClure crossed the plate when Rienzo threw a wild pitch to Ryan Eigsti, but he struck Eigsti out to end the frame.
"I put pressure on myself when I had runners on second and third base," he said of the errant pitch. "The catcher [Luis Sierra] tried to stop the ball, but it was my fault.
"I pitched well, but the other team was good. I don't care about [a perfect game]. I just want to help the team win."
Rienzo struck out two more in the sixth and got three fly balls in the seventh before giving way to Taylor Thompson (1-1), who gave up three runs in the eighth and ended up with a blown save and the loss.
Rienzo started in the White Sox system as an 18-year-old in the Dominican Summer League in 2007, but last year marked his first full season in the United States.
He went 8-4 with a 3.65 ERA with Class A Kannapolis and twice struck out a career-high 10. He struck out eight batters or more nine times last season.
Even though he is still without a Carolina League victory, Rienzo is pleased with the direction his career has taken.
"It was my dream to play baseball in America," he said. "I remember watching my brother play when I was 6 years old and I fell in love with baseball.
"I like soccer, but I love baseball. In Brazil there are no professional teams, so I always hoped I could come to the Major Leagues. Now my dream is here."