Gallo, the top prospect in the Rangers organization, made the jump from Double-A Frisco for what is supposed to be a short stint while four-time All-Star third baseman Adrian Beltre is on the 15-day disabled list with a sprained left thumb.
With the bases loaded in the first, Gallo hit a hard shot that got past Gold Glove first baseman Adam LaRoche. It was scored a "bad-hop single" that drove home the first two runs off Jeff Samardzija (4-3).
When Gallo came up two innings later, he hit the first pitch into the upper deck in right field -- an estimated 418 feet -- for a 6-2 lead.
He came oh so close to another homer in the fifth with a drive that ricocheted off the top of the wall in right-center, after "The Natural" music played for home runs started briefly before being turned off.
"He has impressive power that I think we're all jealous of up here," Beltre said before the game.
Shin-Soo Choo and Carlos Corporan homered for the Rangers, who have won 11 of their last 13 games.
Corporan, who entered the game in the third inning after starting catcher Robinson Chirinos (bruised right hand) was hit by a pitch, had a two-run single in the sixth and added a three-run homer in the eighth. Choo's solo homer came in the fourth, and he had an RBI single in the sixth.
Colby Lewis (5-3) limited the White Sox to two runs over seven innings, with four strikeouts and no walks.
The only runs off Lewis came on Adam Eaton's two-run homer in the third, also in the upper deck in right but not as far as Gallo's.
Samardzija allowed nine runs and 12 hits, both career highs over 233 games -- 110 starts -- since his major league debut in 2008.
Beltre was put on the disabled list, effective Monday, after spraining his thumb sliding into a base Sunday.
The Rangers announced Monday that the 21-year-old Gallo would be called up to get some major league experience with Beltre out, instead of going to Triple-A Round Rock as planned this week.
Gallo, chosen 39th overall as a supplemental pick in the June 2012 amateur draft, was hitting .314 with nine homers and 31 RBIs in 34 games for Double-A Frisco.
After hitting 40 homers combined in rookie ball and Low-A in 2013, Gallo set a Rangers minor league record with 42 last year between High-A Myrtle Beach and Frisco. He was the first player since White Sox prospect Ron Kittle in 1981-82 with consecutive 40-homer season in the minors.
White Sox: Chicago 1B Jose Abreu was held out of the lineup for the third straight game because of a swollen right index finger. Manager Robin Ventura said Abreu could probably play, but that "one swing could probably set him back for five more days." Abreu could be back in the lineup Wednesday.
Rangers: Slugger Josh Hamilton was out with tightness in his left hamstring, a move he called precautionary. He got treatment Monday and Tuesday, and plans to reassess how he feels Wednesday. ... LHP Matt Harrison (spinal fusion surgery) and OF/1B Ryan Rua (right heel) start rehab assignments Wednesday with Round Rock.
White Sox: LHP Chris Sale makes his 10th start of the season for Chicago, his fifth on the road.
Rangers: RHP Nick Martinez is coming off his first loss, but looks to extend his club record streak of 16 consecutive starts allowing three earned runs or less.