New York won for the eighth time in nine games and opened a 3 1/2-game lead over second-place Atlanta in the NL East. The teams begin a four-day, five-game series Thursday in New York.
''They're a really good team and they're playing good baseball, but we're a really good team and we're playing good baseball,'' Vogelbach said. ''I just think you take it as you're playing another game and you're playing another series.''
Chris Bassitt (8-7) pitched seven shutout innings for New York, which finished with 14 hits.
Mychal Givens, acquired Tuesday in a trade with the Chicago Cubs, entered in the ninth and surrendered solo homers to Keibert Ruiz and Lane Thomas in his Mets debut. Givens was charged with five runs, and Seth Lugo recorded the final out.
''We made it exciting at the end, but obviously it wasn't enough,'' Washington manager Dave Martinez said.
Washington lost for the fifth time in seven games a day after it traded star outfielder Juan Soto and first baseman Josh Bell to San Diego. The Nationals dropped to a major league-worst 36-70, including a 9-38 record against the NL East.
New York went ahead in the third when Francisco Lindor worked a nine-pitch walk against Anibal Sanchez (0-4) and Alonso sent the next pitch over the wall in center. Alonso is 6 for 11 (.545) with three homers lifetime against Sanchez.
The Mets broke it open in the fifth after they loaded the bases on a walk, an error and an intentional pass to Alonso. Martinez then replaced Sanchez with Jordan Weems.
Vogelbach drove Weems' fifth pitch into the Nationals' bullpen in right for his third career grand slam. It was Vogelbach's first homer since he was acquired in a July 22 trade with Pittsburgh.
''It's easy to feel comfortable when you come into a team like this,'' said Vogelbach, who is hitting .308 in nine games with the Mets. ''Not just the players on the field, but the players off the field. It's an easy clubhouse to come into.''
Bassitt didn't allow a runner past second base. He permitted six hits, struck out four and walked one.
''He had everything going today,'' Mets manager Buck Showalter said.
Bassitt has pitched 13 shutout innings against Washington this season.
The Nationals hit it into three double plays against the right-hander, bringing their majors-leading total to 103 this season.
Sanchez surrendered five runs - four earned - in 4 1/3 innings. He has dropped each of his four starts since returning from the injured list July 14, and his ERA rose to 7.65.
Mets: Showalter said he anticipates C James McCann (left oblique strain) will return from the injured list Thursday. ... RHP Trevor May (triceps inflammation) was activated from the injured list. May pitched a scoreless eighth. ... The Mets also added 1B/DH Darin Ruf, who was acquired Tuesday from San Francisco, and Givens to the active roster. ... New York optioned RHPs Yoan Lopez and Stephen Nogosek to Triple-A Syracuse and designated INF Kramer Robertson for assignment.
Nationals: RHP Tanner Rainey underwent Tommy John surgery. Rainey went on the injured list July 13. ... 1B Luke Voit, who was acquired in the deal that sent Bell and Soto to San Diego, will join the team Thursday in Philadelphia. ... DH Nelson Cruz (stiff neck) was out of the lineup.
Mets: RHP Carlos Carrasco (11-4, 3.79 ERA), who has thrown 18 2/3 scoreless innings over his last three outings, starts as New York returns home to face Atlanta.
Nationals: RHP Paolo Espino (0-3, 3.78 ERA) gets the nod as Washington begins a four-game series at Philadelphia. Espino is 0-3 with a 4.95 ERA since entering the rotation June 12.
More AP MLB: https://apnews.com/hub/MLB and https://twitter.com/AP-Sports
Copyright 2022 STATS LLC and Associated Press. Any commercial use or distribution without the express written consent of STATS LLC and Associated Press is strictly prohibited.