Yuniesky Betancourt also cracked a solo home run for the Brewers, winners in four of their last five games.
Yovani Gallardo (17-10) worked six spectacular innings, giving up one run on two hits, while fanning a career-high 13 batters.
"He got after it," Brewers manager Ron Roenicke said. "He had a good fastball, good location and a really nice curveball. He really threw the ball well."
The win, coupled with a loss by the St. Louis Cardinals, gave Milwaukee a 6 1/2 game lead in the race for the National League Central crown.
Yonder Alonso homered for the Reds, losers of two straight and six of 10.
Edinson Volquez (5-6) was tagged with the loss after giving up five runs on six hits over 6 2/3 innings. He struck out six and walked three.
The Brewers took the lead for good in the fourth when Betancourt blasted a two-out, solo homer just over the wall in right-center for his 12th home run of the year, giving the Brewers a 2-1 advantage.
Milwaukee widened its lead in the sixth when Nyjer Morgan slapped a single to right to leadoff the frame and swiped second. Prince Fielder was intentionally walked two batter later and after a McGehee strikeout, Betancourt singled home Morgan for a 3-1 lead.
Craig Counsell walked to begin the Brewers' seventh and moved to second on a sacrifice bunt. Morgan was plunked by Volquez two batters later and Jose Arredondo was summoned from the Reds bullpen to face Braun with two outs. Braun made Arredondo pay for serving up a fastball right down the heart of the plate, as he crushed it deep into the seats in left to give the Brewers a comfortable 6-1 advantage.
"You have to get the first guy out," Volquez said of his crucial walk to Counsell. "I walked the first guy, then hit the other guy, and by then I was over 100 pitches."
In the eighth, the Brewers cemented the game when Kotsay smashed a three-run double off the wall in right-center. Morgan singled home Kotsay to account for the final margin.
Earlier, Milwaukee opened the scoring in its first at-bat when Corey Hart ripped a double to start the game and came around to score on a single by Braun. Cincinnati evened the score in the second courtesy of a leadoff home run by Alonso, his fifth of the season.
Reds manager Dusty Baker is one win shy of 1,480 for his career...The Reds are 40-37 at home this season, while Milwaukee is 37-40 on the road...It was Braun's 31st home run of the season...Prior to the game, the Reds honored Hall of Fame catcher Johnny Bench with a statue unveiling outside of the stadium.