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.
