Rizzo doubled in three runs in the Cubs' four-run fifth inning, then broke a 6-6 tie with a three-run homer into the Chase Field swimming pool area off Enrique Burgos (0-2) in the ninth.
Jason Motte (2-1) pitched two-thirds of an inning to get the win. Pedro Strop pitched a perfect ninth for his first save of the season.
The Cubs, losers 5-4 in 13 innings Friday night, scored five runs in the final two innings.
Rizzo's six RBIs tied a career best set on Sept. 16, 2012.
David Peralta doubled in three runs, and Tuffy Gosewisch homered for Arizona.
Copyright 2015 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.