Jose Abreu hit a two-run homer in the first for the White Sox, who head home for a weekend series against the Yankees after a 7-1 road trip moved them into contention for an AL wild card.
The first five batters reached in Boston's four-run sixth before Sale (9-6) was lifted. He allowed seven runs and 12 hits in his worst start since April.
All signs pointed to the White Sox completing their first unbeaten road trip of eight or more games since 1951 and reaching .500 for the first time since early May.
Sale had a sparkling 0.89 ERA in seven appearances against AL-worst Boston. Wright had lost two straight starts since being called up from the minors and the Red Sox were uncompetitive in losing the first three games of the series.
But Sale struggled with his location, while Wright struck out a career-high eight after a suspect start.
The White Sox, who had four-, five- and two-run first innings in the first three games of the series, added two more when Abreu sent a 1-1 pitch into the Red Sox bullpen for his 17th homer. It also extended his hitting streak to 10 games.
But unlike much of the past week, the Red Sox rallied in a game delayed 51 minutes at the start due to rain.
Ortiz, who entered hitting .162 against left-handers, pulled a 98 mph fastball to right for an RBI double in the first. Then Hanley Ramirez and Ortiz had two-out RBI singles in the fifth to put Boston ahead 3-2.
The Red Sox snapped a three-game losing streak, but not without another bizarre injury involving slumping Pablo Sandoval.
The third baseman, who left Wednesday's game with dehydration, was lost to a bruised left forearm after he was plunked while striking out on Sale's inside fastball to end the fourth.
White Sox: Sale stayed in the game after Bogaerts lined a 95 mph fastball off his leg for a single in the first inning.
Red Sox: OF Mookie Betts (concussion) was "slightly improved" but still experiencing headaches Thursday, manager John Farrell said. Betts was hurt tumbling over the wall in Tuesday's game. . RHP Clay Buchholz (shoulder) is still two weeks from picking up a ball.
WHITE SOX MOVES
Chicago manager Robin Ventura thinks his players can block out the distractions surrounding Friday's non-waiver trade deadline.
"Even though they can watch the news and see everything else, their focus is on playing Boston," Ventura said.
The White Sox did make a minor deal, acquiring INF Justin Sellers from Pittsburgh for a player to be named or cash and assigned him to Triple-A Charlotte.
White Sox: LHP Carlos Rodon (4-3, 4.09 ERA) starts Friday's series opener against New York.