With the score tied 1-1 in the eighth inning, Carl Crawford and David Ortiz led off by drawing walks from Leyson Septimo (0-1) and Gonzalez followed by depositing a pitch into the seats above Fenway Park's "Green Monster" wall in left field.
Mike Aviles added an RBI single for the Red Sox, who took the opener of a four-game series.
Chisox starter Dylan Axelrod held Boston to one run on seven hits over 6 2/3 frames, striking out eight.
Kevin Youkilis drove in a run for the White Sox in his first game against Boston since the Red Sox dealt him to Chicago June 25.
2014: The Year in Music [PHOTOS]