Rizzo's homer was a three-run blast, and he finished the game 3-for-5 with five RBIs.
Russell, who went 3-for-3 with two walks, hit a two-run shot in the third as the Cubs swept the three-game series. That broke a Marlins streak of having won four consecutive series before arriving in Chicago.
Jose Quintana (4-2) earned the win, allowing five hits, two walks and one run in six innings.
Chicago's Kris Bryant hit a milestone homer -- No. 100 for his career. The line-drive solo shot to left came on the three-year anniversary of his first major league home run.
Miami starter Wei-Yin Chen (1-2) allowed seven hits, two walks and nine runs in three innings. The eight-run inning he allowed was the worst of his seven-year career.
Chicago opened the scoring with Bryant's first-inning long ball. His homer came on a 1-2 fastball that was up in the zone. It was the 34th time Bryant has hit a two-strike home run.
Chen allowed six hits -- including two to Russell -- in Chicago's game-breaking third inning. Five of those hits went for extra bases.
Russell started the rally with a double. After Albert Almora drew a walk, Bryant hit an RBI double to right-center. Javier Baez singled, and then Rizzo unloaded his homer.
Willson Contreras kept the rally going with a triple that right fielder Brian Anderson lost in the wind. David Bote gave Chicago a 7-0 lead with a sacrifice fly, and the Cubs capped the frame with Russell's homer that followed an Ian Happ walk.
Miami scored in the fourth as Anderson tripled and came home on a groundout by Justin Bour.
But the Cubs kept pouring it on, getting RBI doubles by Rizzo in the fourth and sixth innings. Contreras also hit an RBI double in the sixth.
Miami's Miguel Rojas slugged a two-run homer in the seventh, and Chicago's Bote contributed an RBI single in the eighth.
Marlins backup catcher Bryan Holaday hit a solo homer in the ninth, his first long ball since 2016.
--Field Level Media
Miami | Chi. Cubs | |
Wei-Yin Chen | Player | Jose Quintana |
Loss | W/L | Win |
3.0 | IP | 6.0 |
1 | Strikeouts | 5 |
7 | Hits | 5 |
27.00 | ERA | 1.50 |
Miami | Chi. Cubs | |
Miguel Rojas | Player | Addison Russell |
3 | Hits | 3 |
2 | RBI | 2 |
1 | HR | 1 |
6 | TB | 7 |
.600 | Avg | 1.000 |