Boston won the opener, 11-3.
Chicago was limited to three hits and a run over six innings by Curt Schilling (8-5).
Kevin Youkilis contributed a three-run homer to help carry the Red Sox to their fourth win in five games.
John Danks (6-12) surrendered five runs over 3 1/3 innings to take the loss. It was the 11th setback for the White Sox in 13 games.
Ortiz hit a two-run homer as part of Boston's five-run fourth inning, and then led off the four-run fifth with another blast.