Johnson lowered his major league-leading ERA to 2.87, and the Marlins extended their winning streak to eight with a 4-2 victory over the Milwaukee Brewers on Monday night.
Johnson is trying to become the first rookie to lead the major leagues in ERA since Detroit's Mark Fidrych in 1976.
"If it's there at the end of the year, I'll take pride in that," Johnson said. "For now, I just have to keep going."
Dan Uggla hit his 20th homer and added a sacrifice fly for the Marlins (64-66), who had not been within two games of .500 since they were 1-3 before losing on April 9.
Florida pulled within two games of Cincinnati, the NL wild-card leader, and is one game shy of its longest winning streak of the season. The Marlins start a six-game trip Tuesday at St. Louis.
"Right now we're having fun, and we're just going to keep rolling with it as long as it will go," Uggla said. "This is the time you need to make a run at it."
Johnson (12-6) won his third straight decision, striking out seven in a season-high 7 2/3 innings. He allowed two runs and eight hits. Joe Borowski struck out the side in the ninth for his 31st save in 35 chances.
Milwaukee was swept in a four-game series for the second time this season, following a wipeout in Pittsburgh from May 29 to June 1. Ben Sheets (4-6) gave up three runs -- one earned -- and six hits in seven innings with six strikeouts.
"We faced some good pitching, and we didn't do much with it," Brewers manager Ned Yost said.
Josh Willingham hit a two-out double RBI double in the first, and Florida made it 3-0 with two unearned runs in the fifth.
Cody Ross was on second when he tried to score on Alfredo Amezaga's single, and left fielder Gabe Gross threw a one-bounce strike to the plate. Catcher Mike Rivera failed to hold onto the ball before Ross ran into him, and Uggla followed with a sacrifice fly that scored Amezaga.
"It kind of caught me off guard - the grass here is thinner and faster than at home," Rivera said. "I thought I'd have time to get that hop."
Ross was charged with an error.
"That play cost us two runs," Milwaukee manager Ned Yost said. "He just dropped it. The throw was there in plenty of time."
Bill Hall hit his 30th homer leading off the seventh, and Tony Graffanino's RBI single in the eighth pulled Milwaukee to 3-2 and chased Johnson. Uggla homered off Jose Capellan leading off the bottom half.
"We got some bats on the ball but we couldn't muster up a rally," Hall said. "Johnson threw the ball great."
- Florida tied a team record by winning nine straight from June 10-20.
- Amezaga was in the starting lineup after SS Hanley Ramirez was scratched because of a bruised finger on his right hand.
- The Marlins have seven sweeps, but this was the first four-gamer.
- Johnson and Minnesota's Francisco Liriano are tied for second in wins among rookies, three behind Detroit's Justin Verlander.