Gillaspie hit a run-scoring single in the ninth inning, lifting the White Sox to a 2-1 win over the Marlins on Saturday night.
Peavy (6-2) struck out five and allowed six hits in a complete game, but Derek Dietrich homered with one out in the ninth to tie the game and spoil the shutout bid.
That didn't stop the White Sox, who have won eight of 11 and, at 23-24, are their closest to .500 since April 17, when they were 7-8.
"For us to come back and win in the (ninth) was special," Peavy said. "That's the White Sox way. Nothing's easy around here, is it?"
Through eight innings, Peavy was making it look easy.
Facing a Miami team that entered play hitting .221, Peavy wasn't hassled much. In the second he got a double play with no outs to help him get out of the inning. In the eighth Peavy allowed a one-out double to Greg Dobbs and walked Adeiny Hechavarria but escaped the inning by getting Rob Brantly to pop out and Juan Pierre to fly out.
Other than that, there wasn't much from the Miami offense until Dietrich's homer.
"He pitched great," White Sox manager Robin Ventura said.
Alexei Ramirez gave Chicago a 1-0 lead with an RBI double in the third. Pierre mishandled the ball in the left field corner -- but wasn't charged with an error -- allowing Alejandro De Aza to score from first.
Thanks to Peavy, however, that lone run was all the White Sox needed until the ninth.
Ricky Nolasco allowed one run and eight hits and struck out six in 7 2/3 innings for Miami but couldn't earn his second consecutive win after beating Arizona on May 19. The Marlins right-hander has allowed two runs over his last two starts and kept the White Sox in check.
It wasn't good enough for the win, however.
Wise, who entered as a defensive replacement for Dayan Viciedo in the top of the ninth, led off with a double off Ryan Webb (1-3). He streaked home on Gillaspie's single to left, scoring easily ahead of a throw from Pierre.
"Baseball is such a funny game because everybody feeds off each other," Gillaspie said. "We went through some pretty rough times the first half of the season. It's good to kind of get everybody on the same page. Everybody's excited. You can feel it in the clubhouse."
Miami is going through some rough times now, to say the least.
The Marlins have dropped 11 of their last 13 and have sunk to 13-36, the worst record in the major leagues. They've lost four straight and are in danger of being swept Sunday.
After Dietrich's home run, it appeared the Marlins were headed in the right direction. The drive tied the game and extended Dietrich's streak of reaching base to 14 games, the second-longest streak for any Marlin to start his career behind Kevin Millar's 17 in 1999.
"We finally get a big hit, Dietrich does. Great swing. Great at-bat. He crushed that ball," Marlins manager Mike Redmond said. "I was thinking the momentum is switching to our side and then they come back on four pitches and win the ballgame."
The loss was the second straight one-run defeat for Miami, which is 6-13 in one-run games this year.
"Obviously that's not the way we wanted to go out," Webb said. "It sucks losing two games in a row like that."
White Sox LHP Chris Sale, who was scratched from his start Wednesday, played catch off flat ground Saturday. He's expected to throw a bullpen session Sunday and start Tuesday. . Marlins RHP Nathan Eovaldi pitched five innings and struck out five in a rehab start at Class-A Jupiter. Eovaldi hasn't pitched in the majors this season after going on the DL with right shoulder inflammation. ... John Danks, who made his first start for the White Sox in over a year Friday night, said his left shoulder felt good one day after throwing 76 pitches. ... Redmond said 2B Donovan Solano, who was placed on the DL May 7 with a left intercostal strain, will be sent to extended spring training Monday. ... INF Angel Sanchez was outrighted to Triple-A Charlotte after being reinstated from a rehab assignment for lower back spasms. The move clears a spot on Chicago's 40-man roster. ... Chicago's Hector Gimenez started in place of Tyler Flowers for the second straight night. Flowers also missed Friday with back spasms. ... Sunday's pitching matchup is Miami's Alex Sanabia (3-6, 4.56 ERA) against Chicago's Dylan Axelrod (2-3, 4.13).