With the win, the Nationals trimmed their magic number -- the combination of wins they need and losses needed by their closest competitor to make the playoffs -- to three games.
"There are still seven games left," Corbin told reporters, according to MLB.com. "Guys are focused on that. Even if we do clinch here, we still want to play good baseball, clean baseball. That's what guys here will be doing."
Eaton smashed a 443-foot solo homer in the Nationals' second at-bat of the game, sending the shot out of the park at 108 mph, according to Statcast. Gomes hit a 407-foot solo shot in the Nationals' third at-bat of the second inning, giving Washington a 2-0 lead. Turner led off the bottom of the third inning with another solo shot, smacking an 0-1 Zach Eflin fastball over the left center field fence for a 388-foot blast.
The Nationals added two runs in the fifth frame to take a 5-0 edge. The Phillies scored their first run in the sixth inning after a throwing error. Phillies reliever Edubray Ramos issued two walks with the bases loaded in the eighth inning, giving Washington a 7-1 advantage.
Phillies catcher Andrew Knapp plated the final run of the game with an RBI double in the top of the ninth inning.
Eflin allowed eight hits and five runs in five innings for the Phillies. Eaton went 3 for 4 with two runs scored, an RBI and a walk for Washington. Anthony Rendon went 1 for 3 with two RBIs and two walks in the win.
The Nationals host the Phillies at 1:05 p.m. EDT Tuesday in Washington, D.C.