Baez opened the bottom of the ninth with a double off Wandy Peralta (3-3) and pinch-hitter Jon Jay walked. Then, Ben Zobrist moved the runners with a groundout.
Reliever Blake Wood came in and struck out Albert Almora Jr. With two outs and Kris Bryant batting, Wood threw a breaking pitch that got away from catcher Tucker Barnhart for the game winner.
Wade Davis (3-1) pitched a perfect ninth, redeeming a bullpen that nearly spoiled John Lackey's strong outing by giving up three home runs and surrendering a five-run lead.
The third career grand slam of Rizzo's career came after both teams loaded the bases with their first three batters of the game.
The Reds managed just one run in the top of the first, while Rizzo regained the lead for Lackey with an opposite field blast, his 28th of the season.
