Sweeney began the day hitting .119 with two RBIs in exhibition play. He homered off Felipe Paulino to start the second inning.
Paulino went four innings, allowing three runs and five hits. He will start the second game of the season for the White Sox.
Adam Dunn and Dayan Viciedo hit back-to-back home runs, the first of the spring for both of them, off Wesley Wright in the White Sox ninth.
The crowd of 15,170 pushed the spring total to 213,815 at Cubs Park for a single-season Cactus League record. In their first season at the ballpark, the Cubs broke the mark of 203,105 they set at HoHoKam Stadium in 2009.