Brian Goodwin is all smiles after his home run in the eighth inning gave the Nationals the lead over the Marlins. (Carolyn Kaster/Associated Press)

As Miami Marlins second baseman Dee Gordon’s line drive sunk toward the earth, and young Washington Nationals left fielder Andrew Stevenson closed in pursuit, Manager Dusty Baker said his mind raced.

I hope he catches it, to stop the tying run from scoring from third. If he doesn’t catch it, I hope it stays in front, or Gordon will circle the bases. If Gordon gets on, do we pitch to Giancarlo Stanton, the only one to do any damage against us all day?

But as all those scenarios whirled around in a cyclone of unpleasant possibilities, Stevenson dove, scooping them up before the ground could turn them into unpleasant realities, thereby clinching the Nationals’ 3-2 win.

“I was glad I didn’t have to make those decisions,” said Baker, who has watched injuries threaten to pull his veteran team back to earth, only to have youngsters like Stevenson lift it from the brink again and again.

Stevenson’s catch earned Sean Doolittle his seventh save in seven chances as a National. It earned the Nationals their third win in four games against their closest National League East competition and built their division lead to 15 games.

That catch preserved a one-run lead built by another rookie, center fielder Brian Goodwin, who found regular playing time in June, when Jayson Werth got hurt, then took over as the everyday center fielder and leadoff man in July, when Michael A. Taylor went down.

After driving in the Nationals’ first run with a single in the sixth, Goodwin provided the go-ahead run with a second-deck home run in the eighth. That was Goodwin’s 13th homer of the season. As of June 1, he had never hit a home run in the majors. Goodwin, who nearly fell off the big league radar after a rough spring training, now has an .816 on-base-plus-slugging percentage, fourth best among qualified National League rookies.

“How many teams can lose two center fielders and then the next one steps up?” Baker said. “Tonight was a game of our youth.”

Stevenson wasn’t in the game when it began. He replaced Adam Lind as a pinch runner in the seventh, then took over for the slower veteran in left field. Lind wasn’t supposed to play as much left field as he has, either, but recently acquired Howie Kendrick is nursing a bad back. Werth is out with injury, Taylor isn’t available, Ryan Raburn is on the disabled list, Adam Eaton is out for the year, rookie Rafael Bautista hurt his hamstring . . . and so on.

That Stevenson is in the majors at all is evidence of the way injuries have poked holes in this Nationals outfielding corps and their roster in general. Stevenson was in the Arizona Fall League last year and began this year at Class AA Harrisburg, an invitee to major league spring training but just barely in the top 10 on the Nationals’ outfield depth chart.

When the Nationals called him up, Stevenson was hitting .246 in 73 games in Class AAA. The Nationals expect him to adjust offensively — he has at every level, and they moved him up quickly. But when Raburn and Chris Heisey hit the disabled list a few weeks ago, the Nationals called up Stevenson because he is known as a plus defender, a guy who can play all three positions — and, potentially, be a late-inning defensive replacement.

He became exactly that after entering in the seventh. Tanner Roark threw six innings and allowed just two runs — Stanton’s third home run in four games — scattered four hits and walked five. He left in a tie game because Adrian Sanchez snuck a double up the left field line to start the sixth, Goodwin singled him home, and with first base open, Bryce Harper doubled to tie it. Marlins Manager Don Mattingly said later he wanted to pitch around Harper, but his starter, Dan Straily, missed the sign.

Brandon Kintzler’s scoreless seventh kept the game tied. Ryan Madson’s scoreless eighth left it that way for Goodwin, whose home run unofficially summoned Doolittle with a one-run lead.

A soft, blooping double put Doolittle in a jam, and a broken-bat groundball moved the tying run to third. Then 72-year-old coach Davey Lopes, the oldest person in the Nationals’ dugout, the most veteran of a most veteran team, asked his 23-year-old left fielder to take a few extra steps toward the foul line — a few steps more than the several he would usually take for Gordon.

“I was like: ‘Oh, no,’” said Doolittle, who glanced up at a replay as he talked about it later. “I turned around, and Stevenson had him played perfectly. . . . It was pretty awesome.”

Stevenson crawled to his feet with the ball secure, face straight as if trying to act like he’d been there before, though Daniel Murphy felt no such need, and just threw both arms in the air in celebration. He is aching, too, these days, and went 0 for 3 in his first game back since missing two with a sore hip. Veterans like him carried the Nationals for much of this season. The youngsters are carrying them now.