Eaton hit his career-high 15th homer during his second three-hit game in three days, and the Nationals beat the Philadelphia Phillies 7-2 on Monday night to strengthen their playoff positioning.
Eaton connected for a solo drive in the first inning. He is 7 for 14 in his last three games.
"That ball he hit, that was a rocket," manager Dave Martinez said. "Upper deck. Line drive. He hit the ball really well today."
Yan Gomes and Trea Turner also homered for Washington, which moved a half-game ahead of idle Milwaukee for the top spot in the wild-card standings. The Nationals reduced their magic number to clinch a playoff berth to three in the opener of a five-game series.
Philadelphia was pushed to the brink of elimination after beginning the season with great expectations after signing former Washington slugger Bryce Harper to a blockbuster deal. The Phillies have to win their final seven games -- including both ends of a day-night doubleheader on Tuesday -- while Milwaukee or Washington loses out to have any hope of reaching the wild-card game.
"I have zero doubts about our guys pushing hard every single game, and as long as we are still in this thing, we are going to act like we're still in it," manager Gabe Kapler said. "We are going to keep fighting. Again, come out tomorrow, win a couple games and you never know what can happen, and that's the way we're thinking about it. We're still in this."
Washington left-hander Patrick Corbin (14-7) matched his career high for wins in the first season of a $140 million, six-year contract. He allowed one run and three hits in six innings.
"My fastball felt really good today," Corbin said. "I was able to locate it. I thought some two-seamers were close, just missing a little bit, but felt really good about it. Just kind of kept them off balance. Didn't want to leave any breaking balls there for them to do some damage with. So, kind of a little bit of everything."
Corbin elicited his loudest cheer of the night when he struck out Harper to end the third. The former Nationals star, who is playing his third series in Washington since joining the Phillies in March, was booed before each of his plate appearances. He went 1 for 3 with a walk.
Corbin also won 14 games in 2013 and 2017 while pitching for Arizona.
Gomes went deep in the second and Turner connected in the third against Zach Eflin (9-13), who was charged with five runs and eight hits in five innings.
"For the most part, I thought I did a really bad job of setting the tone in the game and the series," Eflin said.
Phillies: C J.T. Realmuto was out of the lineup with right knee soreness. He was scheduled to undergo an MRI exam. "I don't want to take any chances," Realmuto said. "I don't see it being anything too serious. I should feel better tomorrow." ... RHP Juan Nicasio (rotator cuff tendinitis) could be available in the next few days, Kapler said. ... RHP Seranthony Dominguez (elbow) threw a bullpen session. ... OF Roman Quinn (groin strain) ran 80-yard sprints and could return later this week.
Nationals: C Kurt Suzuki (elbow) threw hard from 120 feet on back-to-back days and for the third time in four days. Bench coach Chip Hale said Suzuki was on track to start the second game of Tuesday's day-night doubleheader.
Phillies: RHP Blake Parker (3-2, 4.40 ERA) will start for the first time in Tuesday's first game after making 286 career relief appearances. RHP Aaron Nola (12-6, 3.75 ERA) will start the second game.
Nationals: RHP Joe Ross (3-4, 6.17 ERA) gets the nod in the first game in his first appearance since Sept. 2. RHP Max Scherzer (10-7, 2.81 ERA), who has 19 strikeouts in 12 innings against Philadelphia this season, will get the ball in the night game.
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