Rizzo scored three times and Alfonso Soriano contributed three hits and two RBI for the Cubs.
Jeff Beliveau (1-0) earned his first major league win despite allowing a three-run homer to Pedro Alvarez in the sixth inning that put the Pirates ahead 9-5.
Pittsburgh's Jared Hughes (2-2) was tagged with the loss after yielding Rizzo's second shot -- a three run blast in the bottom of the sixth.
Alvarez finished with two homers as the Bucs lost for the eighth time in nine contests.
Notable deaths of 2014 [PHOTOS]