Holmberg pitched six innings of two-hit ball in his first major league win, and the Reds stopped Milwaukee's three-game winning streak with a 5-1 victory on Saturday night.
Holmberg's fastball tops out at about 89 mph, but the 23-year-old left-hander effectively changed speeds to frustrate a Brewers lineup stacked with strong right-handed hitters.
Holmberg (1-1) impressed in an audition for 2015 for the Reds, who are seven games under .500.
"I just believe this September is hugely important for David simply to have the opportunity to pitch and get more comfortable as we head into 2015," manager Bryan Price said. "He's taking advantage of his opportunities."
Holmberg struck out four and walked two. He has yielded just one earned run in 12 2/3 innings over three September appearances.
The Brewers' offense is struggling as they try to keep pace in the National League playoff race. Milwaukee remained 1 1/2 games behind Pittsburgh for the second NL wild-card spot after the Pirates lost 6-4 to the Cubs.
"I can't explain it. He threw the ball well," Ramirez said about Holmberg. "What can I say?"
Holmberg overcame an early bout of wildness after hitting two batters in the first, when the Brewers also had their best chance at a big inning.
Cozart threw to second for a forceout before Cincinnati tracked down Gomez in a rundown. Holmberg then got Khris Davis to fly out to right to end the inning.
When he got into trouble, Holmberg started thinking about what pitching coach Jeff Pico told him in the bullpen before the game.
"I was spinning off pitches and that was making me wild," Holmberg said. "I just wanted to get back in the zone and make pitches."
Cincinnati scratched out two runs in the fourth on a bases-loaded walk and sacrifice fly off Yovani Gallardo (8-10). But the speedy Hamilton broke open a one-run game with his triple to the gap in right-center in the seventh.
Hamilton's first extra-base hit since Aug. 28 came against Zach Duke, part of a porous outing for a Brewers bullpen that gave up three runs and six hits combined in the seventh and eighth innings.
A frustrating night at the plate for Milwaukee included a corkscrew swing for Gomez through a Holmberg curveball for a strikeout. Gomez's helmet fell off during the swing, and the animated outfielder slammed his bat down on the helmet on the ground before walking away.
The Brewers haven't scored more than four runs in a game since beating St. Louis 6-2 on Sept. 5.
"It's hard to say what it is that's going to take us to bust out and swing the bat well," manager Ron Roenicke said. "I know we're facing tough pitching so I'm not expecting big numbers every night but I expect guys to swing the bat."
Reds: 1B Joey Votto rejoined the team this weekend in Milwaukee in an effort to return before the end of the season. Votto, who has been on the disabled list since July 8 with a left knee injury, worked out before Saturday's game.
Brewers: Right-handed hitter Ryan Braun was moved up to the No. 2 spot in the order against the lefty Holmberg. Roenicke also said he liked how Braun has swung the bat since the outfielder got a day off to rest a nagging right thumb injury.
Reds: RHP Mike Leake (11-11) is scheduled to make his career-best 31st start on Sunday. He already has career highs of 149 strikeouts in 196 1/3 innings.
Brewers: RHP Matt Garza (7-8) is 1-0 with a 0.56 ERA in two starts this season against Cincinnati.
Follow Genaro Armas at http://twitter.com/GArmasAP