Hart had struck out three times against Lee on Thursday night, but he hit a grand slam with two outs in the eighth inning off reliever Josh Lindblom, and the Brewers beat the Phillies 7-4.
Lee was removed after an error with two outs in the eighth kept the inning alive. Lindblom (2-3) entered the game and loaded the bases before Hart hit a 2-2 pitch just over the wall in right to snap Milwaukee's three-game losing streak.
"It was a terrible night; now it's turned into a great night," Hart said. "Striking out has become part of my repertoire, but big hits, you can't beat it."
Weeks reached second, and Philadelphia manager Charlie Manuel summoned Lindblom to face Ryan Braun, who had hit two homers off Lee. Braun was intentionally walked, and Aramis Ramirez walked to load the bases.
Domonic Brown couldn't make the leaping catch of Hart's drive. It was Milwaukee's fourth home run of the game after Lee gave up three solo shots but little else.
"He was great tonight," Hart said of Lee. "He, obviously, left up a few balls for our guys to hit. I wasn't one of the guys. He was dominating me. I was happy for him to get out of there.
"Lindblom's been tough, but after the rough night I had, I was excited that anybody but Cliff was out there," he said.
Since being acquired from the Los Angeles Dodgers on July 31, Lindblom has given up six earned runs in five innings over seven appearances.
"I haven't made pitches; I haven't executed," Lindblom said. "There's really no excuses other than the fact that you just got to go out and make pitches."
Lee said he understood why Manuel removed him.
"I felt good, but it wasn't really debatable," Lee said. "Charlie came out there and said, 'We're going to go with a rightie.'
"Obviously, if he asks me how I feel, what I think, I'm going to tell him I want to keep pitching," he said. "It wasn't really up for debate. He kind of had his mind made up. And considering Braun is 2-for-3 with two home runs, it actually made some sense."
Livan Hernandez (4-1) pitched a scoreless eighth for the victory. Jim Henderson recorded the final two outs for his third save in four chances, getting Erik Kratz to ground out with the bases loaded to end the game.
"I hope it calms down a little bit," Milwaukee manager Ron Roenicke said of his bullpen's inability to record an easy save.
Lee allowed two solo home runs by Braun and a solo homer by Ramirez but pitched 7 2/3 innings, giving up five hits without walking a batter and striking out 12. He was in line for only his third win in 22 starts until Hart's late heroics.
The homers by Braun and Ramirez allowed the Brewers to open a 3-1 lead, but Philadelphia took the lead on Frandsen's two-out double off Milwaukee starter Marco Estrada in the fifth. The right-hander recorded the first two outs of the inning and then fell apart.
Ryan Howard singled to left, Brown walked and Laynce Nix singled to load the bases. Frandsen, recalled from the minor leagues when Placido Polanco went on the disabled list July 27, hit a 3-2 pitch to the gap in left-center field, with all runners easily scoring to give the Phillies a 4-3 lead.
Estrada took 108 pitches to get through five innings, giving up four runs, eight hits and three walks while striking out one.
Braun took early batting practice nearly four hours before the game in an attempt to snap out of a 9-for-47 slump with no walks and no home runs in his previous 49 plate appearances. The NL MVP hit an 0-2 pitch from Lee off the top of the wall in right-center for his 30th homer, which gave Milwaukee a 1-0 lead.
Ramirez followed with a homer to center, his 16th, to make it 2-0.
Philadelphia pulled within 2-1 in the third when Jimmy Rollins scored from third on a fielder's choice.
Braun then hit his second homer of the game in the fourth on an 0-1 pitch, marking his fifth multihomer game this season.
"Their pitchers were able to keep the ball in the ballpark, and we weren't," Lee said. "That's what it really came down to. Braun hit two home runs off me, and Ramirez hit one as well. We've got to do a better job of keeping the ball in the ballpark."
Polanco, out with back inflammation, went 1-for-3 in his first rehab game for Single-A Clearwater. ... Thursday's game was the 50th for Phillies 2B Freddy Galvis in his 50-game suspension for using a performance-enhancing substance. Galvis will be placed on the 15-day DL on Friday for a lower back injury. ... Braun joined Prince Fielder as the only Brewers to have five seasons with at least 30 homers. ... Lee has given up 12 home runs in his past six starts.