CINCINNATI — The Reds managed only two hits in 12 innings, another indignity in their fast-fading season.
Upton's 25th homer off Manny Parra (0-1) gave Atlanta its seventh victory in eight games.
The Reds managed only a pair of singles by Billy Hamilton in their seventh consecutive loss. They fell seven games under .500 for the first time since 2009. Cincinnati (61-68) has dropped out of contention by going 10-24 since the All-Star break.
"It's discouraging, frustrating — whatever word you want to use," manager Bryan Price said.
Aside from Hamilton's two hits, the rest of the Reds' lineup went 0 for 34.
"We're all working hard," said Hamilton, who also stole three bases. "It's just happening the way it's happening."
Minor has only one complete game in his career, but he held the Reds without a hit into the eighth, bidding to become the first Braves pitcher to throw a no-hitter since Kent Mercker in 1994.
Zack Cozart drew Minor's fourth walk and advanced on a groundout. Hamilton lined an RBI single to center with two outs to end the no-hitter on Minor's 107th and final pitch.
"Everything he had was working, every pitch," Hamilton said. "He was hitting his spots. Every pitch was working for him."
Cincinnati's defense kept it in the game even though the Reds couldn't get a hit until late.
Mat Latos gave up nine hits — matching his season high — but limited the Braves to one run in six innings with the help of several run-saving defensive plays.
Upton extended his hitting streak to 13 games with a single, helping the Braves load the bases with one out in the third. Cozart saved at least one run by making a diving stop on Tommy La Stella's grounder to the hole at shortstop and getting a forceout at second, holding Atlanta to one run on the play.
Second baseman Brandon Phillips saved two more runs in the sixth. With runners on second and third and two outs, he made an over-the-shoulder catch of Jason Heyward's fly to shallow right field.
Atlanta (68-61) stranded six runners in scoring position over the first six innings.
Braves: RHP Shae Simmons, who had to quit throwing at Triple-A Gwinnett because the back of his pitching shoulder was bothering him, is back in Atlanta getting treatment. There's no timetable for when he'll resume throwing.
Reds: LHP Tony Cingrani is still having problems with his left shoulder, preventing him from throwing. He was on the DL in May with a sore shoulder, struggled after his return and was optioned to Triple-A Louisville, where his shoulder began bothering him again.
Braves: Ervin Santana (13-6) has won his only other career start against the Reds, beating them 5-4 on April 25 at Turner Field.
Reds: Mike Leake (9-11) is trying for his first win since Aug. 3. He's 0-2 with a no-decision in his last three starts.
CHEERS FOR THE COMMISSIONER
Commissioner Bud Selig was applauded by the crowd of 31,160 when he was shown on the videoboard after the first inning, sitting next to Hall of Famer Joe Morgan and Reds owner Bob Castellini. Selig was in town to help dedicate an urban youth academy.
Minor's 7 2-3 innings were a season high. ... Upton is batting .413 during his streak. He also had a triple on Friday. ... The Reds are 0-5 against Atlanta this season, their most losses to the Braves since 2005. ... Cincinnati is 3-9 in extra-inning games, losing its last six. ... Phillips is 3 for 20 in four games since returning from a torn ligament in his left thumb.
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