Fernandez struck out 11 over seven innings and drove in two runs during a three-run sixth to help Miami defeat the Washington Nationals 5-1.
More importantly to him, Stanton and Ozuna survived their tangle that led to Ryan Zimmerman's inside-the-park home run for Washington, and then contributed to Miami's three-run rally.
"That was scary, very scary for us as a team, and not fun to watch," said Fernandez, who allowed the run on four hits and three walks while throwing a career-high 117 pitches. "Not a good feeling."
Stanton led off the sixth with his 11th home run. Ozuna singled and scored on Fernandez's single later in the frame, two innings after both he and Stanton were briefly motionless on the Nationals Park warning track.
"It wasn't like a head-on blaster, but you don't really know what happens on that," said Marlins manager Don Mattingly, who was part of the contingent that attended to both players on the field. "Especially when they don't get up. I think that bothers you more than anything."
With no one on against Fernandez, Zimmerman drove a full-count curveball into the gap in right center.
As Stanton and Ozuna chased it, their legs clattered together, sending both tumbling. Stanton crashed into the out-of-town scoreboard and Ozuna hit the ground as the ball fell and Zimmerman scored easily.
"I was looking around for the ball kind of and I didn't really put it together," said Stanton, a three-time All-Star who is in the second of a 13-year, $325 million contract. "I thought he had it, threw it in already. I was a little jacked up for a second."
Fernandez (5-2) struck out 10 and only allowed three balls in play after that moment, fanning the side in the sixth and seventh to help the Marlins secure a four-game split.
The win runs his all-time record against Washington to 5-0 with a 1.09 ERA.
"The whole season as the game has been progressing, I've been feeling better and better every time,"said Fernandez, who pitched through the seventh for a second consecutive start. "I feel like I could've kept pitching."
Nationals starter Joe Ross (3-3) allowed five runs -- three earned -- over 5 2/3 innings.
Washington struck out 15 times, with big league batting leader Daniel Murphy a late scratch due to illness.
"I think the doubleheader yesterday kind of got us all a little bit, and the skipper kind of took it out of my hands and gave me the day," said Murphy, who pinch hit in the ninth. "And personally, I could use that."
HISTORY INSIDE THE PARK
Zimmerman's homer was the first inside-the-park shot and the third since the Nationals started playing in Washington in 2005. It was the 26th in Montreal/Washington franchise history.
Before the game, the Marlins recalled LHP Jarlin Garcia from Triple-A New Orleans and optioned RHP Nick Wittengren there. Garcia did not appear Sunday. When he does, it will be his big league debut.
Marlins: RHP Kendrys Flores was also sent to Triple-A New Orleans after exiting his start Saturday after three innings with a shoulder strain. Flores had been added to the roster as the Marlins' 26th man to pitch the second game of a split doubleheader.
Nationals: Murphy was originally slated to hit fourth in the series finale. He's now batting .400 with five homers and 23 RBI.
Marlins: LHP Adam Conley (2-2, 3.72) looks for his first career victory against the Phillies in the first of three at Citizens Bank Park on Monday. Conley has pitched well against Philadelphia, allowing two runs in 18 IP over three starts.
Rockies rally, win in 10th as Dodgers' bullpen woes continue
— Trevor Story homered and drove in the go-ahead run in the 10th inning as the Colorado Rockies took advantage of the Dodgers' recent bullpen woes, beating Los Angeles 9-6 Friday night.
Blackmon launches 2-run homer in 10th
Charlie Blackmon extends the Rockies' lead with a two-run home run in the 10th inning vs. the Dodgers.
Hilliard's homer gives Rockies lead in 9th
Sam Hilliard finishes off the Rockies' comeback with a solo home run in the top of the ninth vs. the Dodgers.
Raleigh, Torrens hit back-to-back HRs, Mariners top A's 4-3
— Cal Raleigh and Luis Torrens hit back-to-back homers, Dylan Moore scored the go-ahead run on consecutive wild pitches and the Seattle Mariners beat the Oakland Athletics 4-3 on Friday night.
Cal Raleigh demolishes 1st career HR, Mariners go back-to-back
Cal Raleigh sends his first big league home run 444 feet as the Mariners hit back-to-back dingers in the second inning of a 4-3 win over the A's.
Reynolds HR, Pirates stop 4-game skid, beat Giants 6-4
— Bryan Reynolds homered, Adam Frazier drew a bases-loaded walk to force in the go-ahead run in the seventh inning when Pittsburgh scored three times without a hit, and the Pirates beat the San Francisco Giants 6-4 on Friday night.