The A's top prospect surrendered one run on six hits en route to his first win of the season on Monday as the Triple-A Sacramento River Cats beat the Reno Aces, 2-1.
Parker fanned seven and issued two free passes, giving him 17 punchouts and four walks through his first three starts.
The 23-year-old right-hander worked just one perfect inning on the day -- the fourth -- but was able to get out of trouble for the most part. He allowed a runner to reach second base in his five other innings, but the only run he gave up came in the second, when Ryan Wheeler took a 3-1 pitch over the right-field wall.
Pedro Figueroa tossed two scoreless frames, while Jim Miller worked around a fielding error by shortstop Adam Rosales in the ninth for his second save.
Outfielder Michael Taylor went 3-for-4 to raise his average to .413, while Brandon Moss doubled, walked twice and scored a run.
Selected ninth overall by the D-backs in 2007, Parker went 11-8 with a 3.79 ERA in 26 starts for Double-A Mobile last year. He also performed well in the playoffs, yielding just two runs in 12 innings (1.50 ERA) as the BayBears won the Southern League title.
Parker was traded to the A's in December with outfielder Collin Cowgill and pitcher Ryan Cook in exchange for big league veterans Trevor Cahill and Craig Breslow.
The native of Indiana put together a 3.27 ERA in 11 Spring Training innings for Oakland, but he also walked 13 batters. His control problems culminated in his final Cactus League start when he issued seven free passes without a strikeout in 3 2/3 frames. He was sent down later that day.
In 18 innings so far for Sacramento, Parker has a 2.50 ERA. He is likely to be the first pitcher called up by the A's if one of their big league starters struggles or gets injured.