Martin (2-4) allowed seven hits in a career-high 6 2/3 innings in his first win since April 11. The right-hander went 0-3 with a 3.86 ERA in his previous five appearances.
Mike Vasil handled the ninth for his first save in his 13th career game.
Playing in front of a capacity crowd of 43,585 on Pete Rose Night, Cincinnati lost for the ninth time in 11 games. The Reds have scored a total of 16 runs in their last five games, and that includes a 13-9 victory at Houston on Saturday.
Spencer Steer homered for Cincinnati, which went 1 for 9 with runners in scoring position. Steer and Gavin Lux each had two of the team’s nine hits.
The White Sox jumped in front in the second against Nick Lodolo (3-4). Luis Robert Jr. singled, stole second and scored on Andrew Vaughn’s double into the corner in left.
Robert added an RBI single in the fifth, and Sosa connected for his third homer in the sixth. Taylor hit a leadoff drive in the seventh against Scott Barlow.
Lodolo was charged with three runs and seven hits in 5 1/3 innings.
Key moment: Austin Hays hit a two-out RBI double for Cincinnati in the eighth. But Steer flied out to center, ending the inning.
Key stat: The White Sox are 5-17 on the road this season. They went 18-63 on the road last year.