Todd Jones worked a perfect ninth for his 18th save.
Granderson reached base four times, and Marcus Thames hit his 13th home run to extend his hitting streak to nine games.
Cubs backup catcher Henry Blanco and Aramis Ramirez also homered.
Chicsago's Glendon Rusch (2-7) gave up out four runs and six hits in 1 2-3 innings -- his shortest start of the season.
White Sox 12, Reds 4
At Cincinnati, Joe Crede's first-inning grand slam got Chicago's high-powered offense rolling, and the White Sox extended their interleague domination of Cincinnati.
Crede also had a double and a single, and Scott Podsednik drove in three runs with a pair of singles as the White Sox rocked left-hander Brandon Claussen (3-8) and kept on going against Cincinnati's rickety bullpen.
The defending World Series champs have won six of their last eight. They remain 1 1/2 games behind Detroit in the AL Central.
The White Sox are 10-2 against the Reds in interleague play.
White Sox starter Freddy Garcia (8-5), who had been in a deep slump for nearly a month, gave up four runs and seven hits in eight innings, improving to 17-6 with a 2.37 ERA in interleague play.
Orioles 6, Mets 3
At New York, Erik Bedard won his first game in a month and Melvin Mora hit a two-run home run against his former team as Baltimore ended New York's winning streak at eight games.
Mora's two-run shot capped a four-run seventh inning for the Orioles, who had lost three straight.
Alay Soler held Baltimore to four hits over six innings and the Mets were leading 3-2 when Aaron Heilman (0-2) relieved at the start of the seventh.
He got in trouble immediately, walking Kevin Millar and Nick Markakis to start the inning. Brian Roberts' grounder drove in the tying run and Brandon Fahey looped a single to left to give Baltimore a 4-3 lead.
Mora followed with his ninth homer of the season.
Bedard (6-6) last won on May 17 against Boston and had lost his last four decisions. He allowed just three hits over six innings, walking three and striking out six.
Chris Ray pitched a perfect ninth for his 17th save.
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