MILWAUKEE -- Jake McGee was supposed to have the day off on Saturday.

After working in each of the Giants' last two games, the left-hander, who has the third-most saves among National League relievers, was told he'd get some rest as the Giants used a bullpen day in the middle game of their three-game weekend set against the Brewers in Milwaukee.

But as is often the case when people look forward to a relaxing day off, plans changed quickly for McGee, who came on in the 11th inning to protect a four-run lead as the Giants pulled off an unlikely 9-6 victory at American Family Field.

"They told me I'd be down today so I came in, got treatment, but didn't do my stretches," McGee said. "I didn't have my brace down there [in the bullpen] or even my cup. ... They had to run it out to me in extra innings."

Considering what happened to get the Giants to the point of needing him, McGee hardly minded. After all, just about everyone else on San Francisco's roster had been called on in some form or fashion. And by the time McGee finally came into the game, the heaviest lifting had already been done.

San Francisco was one out away from dropping a second consecutive game to the Brewers, who began the day leading the NL Central by seven games and were just three behind the Giants for the National League's best overall record.

But the Giants caught a break with two outs in the ninth when Tommy La Stella's high fly ball to right dropped not into Avisaíl García's glove, but onto the warning track, allowing Kris Bryant to come home with the game-tying run.

And after Tyler Rogers -- working his third game in a row -- shut down Milwaukee in the ninth, the Giants' offense finally sprang to life with three runs, including a two-run single by Buster Posey.

The Brewers stole the momentum in the bottom of the inning, tying things up again with home runs by Luis Urías and Willy Adames. The Giants, however, had one rally left in them, taking the lead for good in the 11th on LaMonte Wade Jr.'s one-out, RBI single before Brandon Belt broke the game open with his second home run of the night and third in two games against Milwaukee.

Having already used eight pitchers on what was a bullpen day, Giants manager Gabe Kapler had little choice but to call on McGee to close things out.

"That was the toughest performance of the year for our club," Kapler said. "Our bullpen was selfless and embodied what we've talked about, which is being unselfish, understanding when the team is going after a big win and picking each other up.

"They all did that. They all stepped up, took the ball in big moments and that's why we're here having this conversation."

Held to just a single run -- a Belt solo home run -- by Corbin Burnes in the series opener Friday night, the Giants' offense was again held to just one run -- a Belt solo shot -- by Burnes' co-ace Brandon Woodruff on Saturday.

The Giants had a prime opportunity to take control of the game and possibly even chase Woodruff early when they followed Belt's home run by loading the bases with one out, but couldn't cash in as Woodruff struck out Mike Yastrzemski and retired Alex Dickerson on a popup to short.

The same duo had a chance again in the sixth. Woodruff had allowed back-to-back singles to Brandon Crawford and Bryant, but left both stranded when Yastrzemski flied out to center and Dickerson struck out.

Despite that, the Giants were still in it thanks to a yeoman effort from their bullpen, which held the Brewers to two runs through the first nine innings.

Aaron Sanchez and Jay Jackson started the group effort, each allowing one run while working two innings apiece. José Álvarez, Zach Littell, Tony Watson and Dominic Leone followed with four scoreless innings.

"The bullpen picked us up and came up big for the group," Kapler said. "Now, we have to come up big for the bullpen."

Having played three consecutive extra-inning games, Kapler admitted that his relief corps is "taxed" heading into Sunday's finale.

"That's part of being in a long season," Kapler said. "It's nice that we have an off-day [Monday]."