WASHINGTON -- Gio Gonzalez became the majors' first 20-game winner in 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.

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 entered Saturday 1 1/2 games behind St. Louis for an NL wild-card berth.

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.

Other than a bit of a pratfall in the seventh -- it wasn't immediately clear why Gonzalez tumbled off the mound and landed face-first in the grass after a pitch -- the lefty 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.

Facing Martin Maldonado 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.

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.

Zimmerman (who hit his 23rd homer), Desmond (24th) and Adam LaRoche (career high-tying 32nd, leading off the sixth inning) 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.

Johnson said he hasn't "put much thought into" the importance of finishing with the NL's best record. Washington began Saturday a half-game ahead of the Central-leading Cincinnati Reds and 3½ ahead of the West-leading Giants.

"I just want to win every game we play. I want to win today. I'll worry about tomorrow, tomorrow," Johnson said. "And I'll worry about who has the best record Oct. 3."

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.

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.

After a walk, Washington made it 3-0 on shortstop Jean Segura's throwing error.

Another walk, this one to Danny Espinosa to load the bases, ended Peralta's day.

Into the game, to warm applause, entered Hernandez, now being used as a reliever but the starting pitcher in the first game in the Nationals' history, back in 2005.

Hernandez got Kurt Suzuki, Washington's ninth batter of the inning, to fly out for the third out.

But then came the fourth. Jayson Werth led off with a single, Harper walked, both advanced on a wild pitch and Zimmerman's shot over the wall in left built the hosts' advantage to 6-0.

It kept getting worse for Hernandez and Milwaukee. After singles by LaRoche and Michael Morse, Desmond made it 9-0. Hernandez was done after getting only two outs and giving up six runs.

The Brewers scored two unearned runs in the sixth. Norichika Aoki doubled leading off, advanced when Weeks' shot to deep center ticked off Harper's glove for what was ruled an error, and scored on Ryan Braun's RBI groundout, before Aramis Ramirez tacked on a sacrifice fly.

In the ninth, Milwaukee's Taylor Green hit a two-run homer off reliever Christian Garcia.

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.