MILWAUKEE -- For seven innings, the Chicago Cubs could do little against Milwaukee Brewers starter Jimmy Nelson.

The right-hander didn't allow a run while holding the Cubs to just two hits -- both of them by first baseman Anthony Rizzo.

When Nelson finally left the game, the Cubs -- especially Rizzo -- seized the moment, notching back-to-back, eighth-inning singles off the Brewers bullpen before Rizzo cashed in with a three-run home run to propelled Chicago to a 5-2 victory in front of a crowd of 36,306 at Miller Park.

"Nelson pitched really well," said Rizzo, who homered for the second time in as many days. "He was holding our guys pretty well down, so we came through there. We got two guys on and got the big inning. Just huge for us."

It was a emotional 36 hours for the Brewers, who thought they lost center fielder Carlos Gomez in a trade with the New York Mets on Wednesday, only for it to fall through later that night.

Gomez reported to the park Thursday, but less than an hour before the first pitch, he was shipped to the Houston Astros, along with right-hander Mike Fiers, in exchange for a quartet of top prospects.

Nelson, though, quickly took fans' minds off the trade and an ensuing rebuilding process.

He walked three but held Chicago scoreless through his first six innings, then worked into a bit of a jam in the seventh, when a leadoff single by Rizzo and two-out walk by catcher David Ross put the tying run on base.

With the pitcher's spot up, Cubs manager Joe Maddon opted to send up pinch hitter Kris Bryant, who was 0-for-6 with two strikeouts against Nelson this season.

Nelson quickly fell behind 2-0 but recovered before Bryant worked the count full, then fouled off a pair of pitches. Nelson finally got him swinging to end the inning and preserve the Brewers' 2-0 lead.

"Everybody knows what he can do with one swing of the bat," said Nelson, who pumped his fist emphatically as he walked back to the dugout. "I felt like that was the game right there. That's probably my last hitter, so I really wanted to get that out and put up another zero."

The Brewers left a runner stranded at third in the seventh, and manager Craig Counsell turned to his bullpen, which had been 36-1 when leading after seven innings this season.

Right-hander Jeremy Jeffress gave up back-to-back singles to second baseman Addison Russell and center fielder Dexter Fowler. With three left-handed batters due up, Counsell called on lefty Will Smith, who left a 1-1 fastball up to Rizzo. The first baseman delivered his 18th home run of the season.

"That hasn't happened too many times this year," Counsell said of his bullpen blowing a late lead.

And while the Cubs' bullpen has been shaky at times this season, it was on its game Thursday. Right-handers Rafael Soriano (2-0), Pedro Strop and Hector Rondon kept the Brewers off the board for the final three innings, with Rondon throwing a perfect ninth for his 14th save of the year.

"There was no messing around, very aggressive, right after them, let's go," Maddon said. "No extra pitches -- I love that part -- very economical."

Chicago made it a three-run game with RBI singles by Fowler and Schwarber in the ninth before Brewers right-hander Michael Blazek got out of the inning.

Milwaukee took an early lead against Cubs right-hander Jake Arrieta with an RBI double by catcher Jonathan Lucroy, who scored on a single by right fielder Ryan Braun in the first.

Arrieta went six innings and allowed two runs on five hits and three walks while striking out six.

NOTES: Less than 24 hours after a deal to ship OF Carlos Gomez to the New York Mets fell apart, the Brewers traded Gomez and RHP Mike Fiers to the Houston Astros for minor league OFs Brett Phillips and Domingo Santana, LHP Josh Hader and RHP Adrian Houser just before Thursday night's game against the Cubs. Gomez is batting .262 this season with eight home runs and 43 RBIs. Fiers is 5-9 with a 3.89 ERA in 21 starts. ... Cubs 3B Kris Bryant was out of the starting lineup. Manager Joe Maddon said it was a day of rest for the rookie, who came off the bench and went 0-for-1 with a sacrifice fly. ... Maddon said C Miguel Montero is improving but likely will go on a rehab assignment before the Cubs bring him off the disabled list. Montero has been sidelined since July 12 due to a sprained left thumb.