Galvis and Erik Kratz each homered off closer Aroldis Chapman in the bottom of the ninth inning Sunday after Lee's baserunning mistake, rallying the Philadelphia Phillies past the Cincinnati Reds for a stunning 3-2 victory.
"As soon as I hit it, it felt good," Galvis, who never had hit a walkoff homer at any level, said. "Awesome. I think I'll never forget it."
Chapman (3-2) blew his second straight save opportunity after converting his first eight chances this season. The 100 mph-throwing left-hander walked pinch-hitter Delmon Young on four pitches to open the ninth.
Lee, the Phillies' left-hander, pinch ran and was caught trying to steal second base, but Chapman wouldn't record another out. Kratz, who entered the game in the third inning after Carlos Ruiz left with a strained right hamstring, pulled a 3-2 pitch over the seats in left to tie it at 2-all.
Galvis followed by lining a 1-1 pitch just inside the foul pole in left.
Lee breathed a sigh of relief after his inexplicable gaffe.
"That's basically the last thing you need to do right there," he said. "It was brutal. I felt horrible. (Winning) was a really good feeling."
Antonio Bastardo (2-1) pitched a scoreless ninth inning for Philadelphia.
"Today's game was definitely a pick me up," said manager Charlie Manuel, whose Phillies open a three-game set at Miami on Monday. "It will give us a nice little ride to Florida."
Slugging first baseman Ryan Howard will not be making the trip to Miami with the team. He's going to have an MRI Monday on his sore left knee.
Howard, who is batting .245 with 46 strikeouts in 151 at-bats this season, has four hits in his last 34 at-bats.
Manuel didn't sound optimistic about Howard's chances to play on Monday.
"We'll see," Howard said. "It's been acting up. I've been able to tough it out but told (Manuel) it was sore."
Ruiz left the game after straining his right hamstring running the bases in the second inning. He didn't make the trip to Miami with the Phillies and will have an MRI on Monday. Ruiz, who said he heard a "pop" while running, hopes to rejoin the team on Tuesday.
"I would've lost a lot of money if I'd bet on that one," Bailey said. "But that's the game."
Bruce led off the second with a towering shot to straightaway center to extend his hitting streak to 10 games. He is batting .390 (16 for 41) with four homers and 12 RBIs during the spurt.
Joey Votto also stayed hot by going 2 for 4 for the Reds. Votto extended his hitting streak to eight games, and he is batting .515 (17 for 33) over the stretch.
Bailey shut down the Phillies for the second time this season and left without a victory for the second time. He allowed five hits with three strikeouts and a walk. He also got a no-decision on April 16 in a 1-0 loss to the Phillies when he pitched eight scoreless innings while allowing two hits with a career high-tying 10 strikeouts and no walks.
"An unfortunate ending, stunning, but that's the game," Reds manager Dusty Baker said. "It kind of spoils you because you always expect (Chapman) to come through. We've got to get him out of the funk he's in and hope it doesn't last too long."
Chapman got off to a rough start Sunday against Young and seemed upset with home plate umpire Tim Welke while facing the Philadelphia pinch hitter, as Welke called at least two close pitches balls.
"I thought I threw good pitches to the first batter," Chapman said through an interpreter.
And the lefty wasn't upset with the location of Galvis' homer, nor did he expect the loss to linger.
"A fastball where I wanted it," he said. "I don't see any problems. Everybody gets hit. Why not me?"
The Phillies looked as if they were on their way to a seventh shutout of the season before the eighth.
Chase Utley's RBI single in the eighth inning snapped the Phillies' 16 scoreless innings skid.
Ben Revere, returning to the starting lineup after sitting out the last four, had three hits for the Phillies. Revere raised his average from .237 to .256.
Jonathan Pettibone gave up two runs -- one earned -- on seven hits in seven innings and has yet to allow more than three earned runs in six career starts.
Philadelphia got to 2-1 in the eighth on Utley's single that scored Revere, but Brown flew out to right with runners on first and second against reliever Sean Marshall to end the threat.
Regular Phillies third baseman Michael Young started at first base for the first time this season. Young went 0 for 3 with a walk.
The Phillies have been shut out six times this season, which is the same total they were blanked in all of 2012. ... The Phillies said right-hander Tyler Cloyd will be called up from Triple-A Lehigh Valley to pitch Tuesday's game at Miami. The team needs a fifth starter with Roy Halladay sidelined after shoulder surgery and John Lannan (knee) on the DL. ... Cincinnati right-hander Johnny Cueto (1-0, 2.60), on the DL since April 15 (strained right lat), is scheduled to face Mets righty Shaun Marcum (0-4, 6.75) when the teams open a three-game series in New York at 7:10 p.m. Monday. ... Phillies lefty Cole Hamels (1-6, 4.61) is slated to oppose Marlins righty Alex Sanabia (2-6, 5.00) at 7:10 p.m. Monday in Miami.