Two winters ago in Hialeah, Fla., the home town that remains deep within him, Gio Gonzalez met the same man each morning at 8:30. The trainer, Sergio Pacheco, carried a folder that outlined Gonzalez’s workout plan. “Intense training,” Gonzalez said. “No breaks.” The cover of the binder bore the title, “Project 20.”

“I sit back and I laugh about it,” Gonzalez said Saturday afternoon, standing at his locker inside the Washington Nationals’ clubhouse.

He had just handed his father, Max, one of the baseballs he used to earn the 20th win of his landmark first season in Washington, a 10-4 demolition of the Milwaukee Brewers. He allowed three hits and no earned runs in seven innings as three homers by his teammates paced him. Gonzalez has played in two all-star games, but to him his 20th win, the thing he had worked all those mornings for, surpassed anything he had done.

“This is like a dream,” Gonzalez said. “I feel like I’m still sleeping in it.”

In the dead of winter, when the Nationals traded for him, a day like Saturday afternoon would have seemed too much to ask: his family in the stands, sun-splashed Nationals Park packed to the brim, a contending opponent made helpless as the Nationals pushed nearer to a division title. It would have seemed too much like a dream.

The Nationals, too, could not have envisioned such a moment. General Manager Mike Rizzo shipped four prospects to the Oakland Athletics for a 27-year-old with nasty stuff and a goofy streak. He has become their ace, a leading Cy Young award candidate, a cherished clubhouse cutup. He leads the majors in wins and moved into a tie for fourth in the National League with a 2.84 ERA. His five strikeouts Saturday brought his season total to 201, making him the first Washington hurler to surpass 200 since Walter Johnson 96 years ago.

“If he was anything like this in Oakland, it’s surprising they got rid of him,” first baseman Adam LaRoche said. “Because this guy is electric.

“This is a big family to him. He cares about everybody. Fun-loving guy. Bulldog on the mound. Just tough not to root for him.”

After Gonzalez warmed up in the bullpen Saturday afternoon, he and pitching coach Steve McCatty walked to the Nationals’ dugout. Manager Davey Johnson asked McCatty: “How’s he feeling? How many do we need to score?”

“He had an awful ’pen,” McCatty said replied. “So that means we probably need one.”

McCatty’s instinct proved accurate. Gonzalez struck out the first batter he faced, Norichika Aoki, flailing at a boomerang curveball. His fastball zipped at 96 mph, “just easy, effortless fuel coming out of his hand,” LaRoche said. The only runs he allowed came after a deep flyball that deflected off Bryce Harper’s glove, a tough play ruled an error.

The outcome was never in question after the third inning. The Nationals had 13 hits, including three-run homers from Ryan Zimmerman and Ian Desmond in the fourth inning off old friend Livan Hernandez, now a Brewers mop-up reliever, in a span of four batters. LaRoche smashed his 32nd homer off Tyler Thornburg, matching his career high. The Nationals led, 9-0, after four innings, and Gonzalez was cruising to his milestone.

“When you can win 20, that’s the mark of Cy Young,” Johnson said. “It’s just everything.”

Wins by a pitcher have been devalued in most corners of statistical analysis, mocked as a contrived metric based more on context than performance. The men who play the game treasure them. After the victory concluded, Gonzalez sought McCatty and wrapped him in a giant bear hug. Teammates tacked $20 bills to the walls of his locker and stuffed them inside his bags.

“It doesn’t feel like a 20th win for myself,” Gonzalez said. “It feels like a 20th win for the team. It’s one of those things you could just smile about it. This is a childhood dream, but at the same to do it with a team that’s in first place, makes it that much better.”

The Atlanta Braves beat the Philadelphia Phillies later in the afternoon, but the Nationals’ victory reduced their magic number to win the National League East to six with 11 games remaining.

Gonzalez’s day included only one hiccup. With one out in the seventh, he clipped a spike on the rubber as he delivered a pitch. The ball flew out of his hand and bounced off the netting high above the backstop. He fell face-first on the mound.

“A perfect 10,” Desmond said. “I’m just glad he didn’t mess up his hair.”

Gonzalez played dead in front of the mound, his face in the grass. As he rose, he stretched his back, causing personnel to rush from the home dugout and 40,493 hearts to drop.

Johnson, McCatty, head trainer Lee Kuntz and the infielders circled Gonzalez. Someone asked if he was hurt. “Absolutely,” Gonzalez replied. “My pride is.”

The huddle dispersed, and Gonzalez tipped to his cap to the roaring crowd. On his next pitch, he struck out Martin Maldonado swinging at a curveball in the dirt.

“You’re giving the fans what they deserve, a show,” Gonzalez said. “Face-first into the floor is definitely what you came to see.”

After Gonzalez polished off the inning, Johnson shook his hand as he returned to the dugout. He watched the remainder, and teammates hugged him upon the last out.

Afterward, Gonzalez thought back to his morning workouts in Hialeah. “I’m still in shock mode,” Gonzalez said. “I’m still emotional right now.” He insisted he would have to come up with a new goal, a higher aim, now that he has accomplished the first one. He has a new team now, and a new place to call home.

“This to me is like saying a thank you to Rizzo for taking a chance with me and giving me an opportunity to play in this great organization,” Gonzalez said. “And I’m not going to stop here.”