Rizzo hit a two-run homer in the first inning off Francisco Liriano, who left in the fourth with discomfort on his side. Rizzo also doubled and scored in the fourth and hit an RBI double in the seventh, a drive to deep right-center that struck Polanco's left wrist as the touted rookie tried to make the catch.
Polanco went 1 for 5 after getting called up from Triple-A Indianapolis, where the right fielder was leading the International League with a .347 batting average and 49 RBIs in 62 games.
Pinch-hitter Luis Valbuena's two-run double off Casey Sadler (0-1) broke a 3-all tie and put Chicago ahead for good.
Travis Wood (6-5) allowed three runs and nine hits in 6 2-3 innings.