On the mound, Wood scattered five hits and two runs over six innings in improving to 5-3. He walked two and struck out six.
White Sox starter Jake Peavy (6-3) was touched for eight hits and six runs over four innings.
Wellington Castillo and Valbuena led off the fourth with singles and Barney was hit by a pitch, loading the bases. Wood hit a 2-1 pitch that just reached the seats beyond left field for a grand slam and 6-1 Cubs lead.
Nate Schierholtz hit a home run for the Cubs in the fifth and Konerko doubled in another for the White Sox in the sixth. Valbuena chipped in an eighth-inning home run and Alejandro De Aza's RBI single in the ninth for the White Sox completed the scoring.
Swim Week Miami Beach 2014 [PHOTOS]