Hart won a salary arbitration case with the team, then followed with a sour spring that only increased the howls against him.
"You get tons of negativity, you get tired of it," Hart said. "But you get through it one way or another. Somehow, I was able to stay positive. It was tough. You never like to be booed, you never like to be questioned whether you should be here or not. I took that as a big chip. I deserve to be here."
Braun's two-run blast in the first set the tone, McGehee drove in his 46th run with his solo homer in the fourth and Hart and Fielder hit consecutive shots in the fifth off Rangers starter Rich Harden (3-3).
"He couldn't get the ball in on those right handers," Rangers manager Ron Washington said.
Milwaukee starter Chris Narveson (5-3) pitched a career-best seven innings and throttled the AL West-leading Rangers, who had won three straight by a combined score of 31-6 over Seattle.
Vladimir Guerrero's solo homer in the second gave him a majors-best 54 RBIs, but Texas' offense sputtered with two hits after the third.
Milwaukee has won four of its last five and got a big game from Narveson, who has barely held onto his spot in the starting rotation after a string of lackluster performances.
"I think being a young pitcher, sometimes you don't realize what it takes or what you need to do," Narveson said. "The sixth, seventh innings, those are the times you've got to make good pitches and if you make a mistake, you've got to come back and keep making quality pitches to get the outs."
The Brewers got the left-hander off to a good start, and his big breaking ball and change up kept the Rangers guessing.
Braun snapped an 11 at-bat hitless streak when he homered off the first pitch he saw from Harden to give Milwaukee a 2-0 lead.
Guerrero answered with his second-inning swat to extend his hitting streak to 10 games, and the Rangers tied it on Michael Young's RBI double in the third.
But Texas, which looked to a tie a season high at seven games over .500, failed to increase its division lead or put up another run even though Julio Borbon (nine) and Josh Hamilton (eight) also extended hitting streaks.
Hart, a former All-Star in 2008, hit .252 with 17 home runs and 81 RBIs after that exhibition game through last year, falling out of favor with the fans and eventually losing his starting job to begin the season after injuries and ineffectiveness.
"He missed a lot of at-bats last year," McGehee said. "He's a special hitter. Obviously, he's got some tools not everybody has. For him to be doing it this consistently is pretty impressive to watch."
In Hart's last 26 games, he has 14 homers and 29 RBIs.
"After the spring training and everything he went through, I don't think the fans were real happy with him," Brewers manager Ken Macha said. "I think it shows you how you can turn it around by going out there and performing.
"I'm happy for him because once again, we're out taking extra (batting practice) and he's out there. He's pretty much locked in and he continues to swing."
McGehee's 10th homer of the season tied Troy Glaus for the NL RBI lead at 46. ... It was the first time Texas had ever played in Miller Park and the teams' first meeting in Milwaukee since the Brewers were in the AL in 1997. ... Hamilton's RBI streak was snapped at seven games. ... Rangers OF Nelson Cruz (left hamstring) is at least a week from going on a rehab assignment after initially hoping to be activated early next week. ... Rangers LHP Derek Holland (left shoulder) continued to suffer lingering pain from a throwing session and returned to Surprise, Ariz. to rehab.