The Cubs won for the third time in four games since they were swept in a weekend series against lowly Philadelphia. Rizzo finished with three hits and Dexter Fowler went 2 for 4.
Smith retired his first two batters, but Rizzo connected for his 18th homer to give the Cubs a 3-2 lead.
The Brewers broke through for two runs in the third against Jake Arrieta. Gerardo Parra led off with a single, giving him a career-high 14-game hitting streak. Parra stole second and scored on Jonathan Lucroy's double. Ryan Braun's infield single drove in Lucroy.
Arrieta gave up five hits in six innings. He is 5-1 with a 1.53 ERA in his last eight starts.
Nelson struck out eight and walked three. He also threw seven scoreless innings in his previous start at Arizona.
The Cubs put two runners on in the seventh but Nelson struck out Bryant swinging to end the inning. Nelson yelled and pumped his right arm as he left the mound to a loud ovation.
Cubs: C Miguel Montero continues to make progress in recovering from a sprained left thumb. Montero has been on the disabled list since July 17. "He's very adamant that he feels really good," manager Joe Maddon said. "There's a lot of issues beyond just catching the baseball. There's legs to be considered, too." Montero likely will be sent on a brief rehab assignment. "I know he doesn't want to do that," Maddon said. ... Bryant didn't start so he could rest. He hit for Arrieta in the seventh and took over at third.
Brewers: After the planned trade of OF Carlos Gomez to the Mets fell apart on Wednesday, Gomez was traded to the Astros prior to the start of the Thursday's game. Milwaukee general manager Doug Melvin bristled at reports that the Mets backed off from the initial deal because of concerns about Gomez's hip. "Carlos Gomez is completely healthy," Melvin said. ... Milwaukee recalled OF Logan Schafer and selected INF/OF Elian Herrera from Triple-A Colorado Springs. They are expected to join the team on Friday.
Cubs: Jason Hammel (5-5, 3.20 ERA) is 6-0 with a 2.25 ERA in eight career starts against the Brewers. He faced Milwaukee in consecutive starts in May, registering a win while surrendering five earned runs over 13 innings.
Brewers: Rookie Taylor Jungmann (5-2, 2.14 ERA) will make his 10th start of the season on Friday night. Milwaukee is 6-3 in those starts. Opponents are batting .210 (43-for-205) with just two home runs against Jungmann.