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WASHINGTON -- Waking up early during the offseason back home in Florida, Gio Gonzalez and his personal trainer would consult a workout program tucked away in a folder labeled "Project 20."

As in 20 victories, a milestone number for a pitcher, even in this age of newfangled statistics.

Gonzalez became the majors' first 20-game winner of 2012, and the first pitcher for a Washington baseball team with 200 strikeouts since Walter Johnson in 1916, taking a shutout into the sixth inning Saturday to help the Nationals close in on their first NL East title by beating the Milwaukee Brewers 10-4.

"In a way, you kind of smile about it, because we finally reached our goal," Gonzalez said, standing in front of a locker sporting seven $20 bills presumably donated by teammates to mark the occasion, "and now it's time to change it up and continue to try and get better goals and higher goals."

Ryan Zimmerman and Ian Desmond each hit a three-run homer off former Nationals pitcher Livan Hernandez in the fourth inning, and Washington stopped Milwaukee's six-game winning streak. The Brewers fell to 2 1/2 games behind St. Louis for an NL wild-card berth.

"I don't feel like we have to win every single game the rest of the season -- I don't feel that -- but I tell you what: We better win most of them or almost all of them," Brewers manager Ron Roenicke said.

Owners of baseball's best record, the Nationals already are assured of postseason play, and Gonzalez (20-8, 2.84 ERA) is a big reason.

"It doesn't feel like a 20th win for myself. It feels like a 20th win for the team," the lefty said. "This is a childhood dream, but at the same time, to do it with a team that's in first place makes it that much better."

Other than a bit of a pratfall -- Gonzalez caught one of his cleats in the dirt, tumbled off the mound and landed face-first in the grass after a pitch -- he was pretty dominant Saturday. He went seven innings, allowing two unearned runs and three hits. He only walked one, and his five strikeouts raised his total to 201.

The Nationals traded for him in the offseason, shipping four prospects to the Oakland Athletics, then signing Gonzalez to a $42 million, five-year deal.

"He's always had the stuff," Zimmerman said.

With one out in the seventh, Gonzalez lost his footing while throwing a pitch that sailed to the backstop on the fly. Gonzalez stayed down on his belly for a few seconds, his arms and legs splayed, before getting up. Eventually, a team trainer, manager Davey Johnson and some smiling teammates went out to check on Gonzalez.

"Oh, it was hilarious. I asked him ... 'Are you hurt?' And he said, 'No, my feelings are hurt a little bit.' So we got a kick out of it," said Nationals first baseman Adam LaRoche, who tied a career high with his 32nd homer.

Added Desmond jokingly: "I'm just glad he didn't mess up his hair."

When Gonzalez stepped back on the mound, he tipped his cap, and the sellout crowd of 40,493 roared. They gave a standing ovation when he walked to the dugout two outs later, his afternoon done. Gonzalez later got a bit hug from Nationals pitching coach Steve McCatty.

Zimmerman (23rd homer), Desmond (24th) and LaRoche are other significant parts of the first major league team in the nation's capital to head to the postseason in 79 years. Washington's victory lowered its magic number for clinching a division championship to six, with second-place Atlanta in action at Philadelphia later Saturday.

Milwaukee starter Wily Peralta (2-1) lasted only 2 2/3 innings, giving up three runs and five hits, along with four walks and a wild pitch.

"He really couldn't get comfortable," Roenicke said. "The mound's a little bit different, and he found that out in the first inning."

Washington's 19-year-old center fielder, Bryce Harper was in the middle of several key plays Saturday. He made a running, back-to-the-infield catch on a deep fly by Rickie Weeks to end the top of the third. Moments later, Harper drove a pitch barely above the dirt into left for an RBI double to make it 1-0. Then, apparently picked off second because he strayed too far off the bag, Harper bolted for third and wound up with a stolen base, before scoring on LaRoche's double.

"Typical Harper move, trying to make something happen," Johnson said. "He probably used that a lot in high school."

Game notes

The Brewers will start RHP Yovani Gallardo (16-8) on Sunday, while the Nationals will use RHP Chien-Ming Wang (2-3) as a spot starter to keep their rotation on regular rest after a doubleheader Wednesday. ... RF Aoki threw out Morse at the plate for the last out of the second. Morse tried to score on Suzuki's fly ball. ... LaRoche also hit 32 homers in 2006, while playing for Atlanta.