Corey Hart singled to begin the 11th inning and scored the go-ahead run from third when
Brandon Phillips bobbled Casey McGehee's ground ball for what was initially ruled an error. The official scorer changed it to a hit following the game.
"Brandon, he's the best there is," said Reds manager Dusty Baker. "Usually he makes that play 99 times out of 100. You figured something happened the way the ball was played."
Rogers, who extended his hitless innings streak to nine, allowed two runs on two hits, walked one and struck out six.
"Pretty impressive outing," said manager Ken Macha. "He has a lot of potential with his arm. His fastball jumps on the hitters. He just needs to focus on the little things like holding runners and being quicker to the plate."
Rickie Weeks hit his 29th home run to break up a no-hit bid by the Reds' Travis Wood in the sixth.
Macha said prior to Friday's game that Rogers was expected to throw 75-80 pitches on Friday. Early on it didn't appear it would take Rogers long to reach his limit.
Rogers needed 21 pitches to get through the first inning, which he began by issuing a walk to Reds center fielder Drew Stubbs.
The speedy Stubbs stole second, advanced to third on a ground out and scored on Joey Votto's sacrifice fly to make the score 1-0.
"I thought he was guiding the ball a little in the first innings," said Macha.
Wood, meanwhile, was perfect through three innings, striking out four.
Rogers was equally dominant, retiring 13 straight after walking Stubbs to begin the game. He did not allow a hit until Jonny Gomes singled with one out in the fifth.
"I settled down a little after the first inning," said Rogers. "It was a great challenge facing [the Reds]. They're division champions for a reason. It was a lot of fun. It was nice to give our team a chance to win tonight."
The Brewers hit the ball hard in the fourth, but had nothing to show for it. Hart's fly ball pushed Jay Bruce to the wall. Ryan Braun scalded a ball to third but Scott Rolen made a back-handed stop.
Rogers flirted with danger in the fourth when Phillips and Votto were retired on warning-track fly balls.
He had 51 pitches entering the fifth when things unraveled.
Gomes singled with one out. Ramon Hernandez's infield hit put runners at first and third.
Paul Janish's perfectly placed squeeze scored Gomes from third making the score 2-0.
Rogers fanned Wood on his 74th pitch to end the inning. He was due to lead off the sixth, but was pinch-hit for by Chris Dickerson.
Weeks brought an emphatic end to Woods' no-hit bid with a 433-foot blast off the facing of the batter's eye in center to make the score 2-1. Wood allowed three runs on three hits in 6 1/3 innings. He walked one and fanned six.
The Reds added to their lead when Stubbs tripled off Jeremy Jeffress to begin the sixth and scored on Phillips' sacrifice fly to put the Reds ahead 3-1.
The Brewers battled back to tie the score in the seventh.
Craig Counsell's pinch-hit single drove home McGehee, who had doubled to make the score 3-2. Jonathan Lucroy followed with a sacrifice fly to left.
The Brewers' rested bullpen held the Reds' offense at bay with five relievers combining for six scoreless innings.
Mike McClendon (2-0) earned the victory. John Axford earned his 24th save.
Rogers isn't likely to begin next season in the starting rotation in order to limit his innings. But Friday night's outing provided a glimpse into his potential as a starter.
"Coming into the season my goal was to be healthy and to finish [in the Major Leagues]," Rogers said. "To have some success is big for my confidence. I took a lot of positives from this September. It was a great opportunity."