Jorge Soler hit two of Miami's four solo homers, helping the Marlins rally for the victory in the rubber game of the weekend set. Garrett Cooper and Jean Segura also connected.
It was Miami's fifth comeback win in its last seven games and No. 20 on the season. The Marlins scored five times in the ninth inning of a 5-1 victory on Saturday.
The Marlins won for the eighth time in nine games overall. They are off to their best start since they also were 37-29 in 2004.
Bryan Hoeing (1-1) pitched a scoreless inning for the win, and A.J. Puk worked a 1-2-3 ninth for his seventh save.
Luis Robert Jr. hit a two-run homer for Chicago, which led 5-1 after seven innings. Romy González hit a tiebreaking two-run double in the sixth, and Jake Burger also had a run-scoring double.
The White Sox wasted a sharp performance by Lucas Giolito, who struck out eight while pitching seven innings of one-run ball. The lanky right-hander is 4-2 with a 3.40 ERA in his last seven starts.
Soler and Cooper started Miami's rally with solo drives in the eighth against Keynan Middleton. It was No. 19 on the year for Soler, who finished with three hits.
Segura led off the ninth with a drive to left against Kendall Graveman (1-3). With two out and runners on first and second, De La Cruz put Miami in front with a double to left.
Chicago played without closer Liam Hendriks , who was placed on the 15-day injured list with elbow inflammation. The three-time All-Star also missed the start of the season while he recovered from non-Hodgkin lymphoma.
White Sox: RHP Jimmy Lambert (right ankle inflammation) was scheduled for an inning in a rehab appearance with Triple-A Charlotte on Sunday. "I think the plan is to just make sure we extend him a little bit, so he can be a multi-inning option if the need arises," manager Pedro Grifol said. "Because right now, we need some length." ... SS Tim Anderson got the day off for rest. ... To replace Hendriks on the roster, LHP Tanner Banks was recalled from Charlotte.
Marlins: Open a three-game set at Seattle on Monday. RHP Bryce Miller (3-3, 4.46 ERA) starts for the Mariners. Miami hasn't announced its rotation for the series.
White Sox: Following an off day, RHP Lance Lynn (4-6, 6.72 ERA) takes the mound for the opener of a three-game series at the Los Angeles Dodgers. RHP Tony Gonsolin (3-1, 2.21 ERA) starts for LA on Tuesday night.