The score was tied at 5 in the 10th when Washington scored the winning run off right-hander Jeurys Familia. With runners on second and third with one out, Ian Desmond hit a sacrifice fly to center fielder Juan Lagares, scoring Jayson Werth.
Left-hander John Lannan entered the game for New York and allowed a three-run homer to Anthony Rendon to make it a four-run game.
"[The fastball] didn't do what I wanted it to do. I really didn't feel any different out there than I did in spring," Lannan said.
The winning pitcher was right-hander Aaron Barrett in his Major League debut. He pitched one shutout inning and struck out two.
"We have confidence in all of our guys," Williams said. "Barrett matched up well against the guys that were coming up. He is ready to pitch every day. We got him out there."
Barrett found winning his first game surreal. His reaction was similar to when he was told that he was on the 25-man roster.
"Talking to the veteran guys, they said, 'Enjoy every minute that [you] can,'" Barrett said. "Today was one of those moments that I've dreamed about -- over and over. It definitely lived up to expectations. I think I'm finally taking a deep breath and finally realizing that just happened to us. It's everything I could imagine for my debut. That was unbelievable."
After looking phenomenal in Spring Training, right-hander Stephen Strasburg was a different pitcher in the first two innings of the opener.
The Mets had runners on first and third in the first when Andrew Brown swung at a 2-2 pitch and hit a three-run homer to give New York a three-run lead.
After Adam LaRoche put Washington on the board with a two-run homer in the top of the second, the Mets added to their lead in the bottom of the inning. Travis d'Arnaud led off with a walk and advanced to second on a single by Ruben Tejada. Starting pitcher Dillon Gee then sacrificed the runners to second and third, and d'Arnaud scored on a sacrifice fly by Eric Young Jr.
That was all the damage the Mets would do against Strasburg, who would last six innings, allowing the four runs on five hits and striking out 10. From the third inning on, Strasburg relied on his offspeed pitches, including his slider.
"Early on Strasburg was up in the zone, and then he found his stride in the third and shut them down the rest of the way," Williams said. "His pitch count got up there and we couldn't run him out there for another inning. He gave us a chance to get back in it."
Other than the second inning, the Nationals had a tough time against Gee, who pitched 6 2/3 innings and allowed four runs on four hits. At one point he retired 15 consecutive batters.
The Nationals put two more runs on the board against Gee in the top of the seventh inning. With runners on first and second and two outs, Rendon blooped a double to right field, scoring Desmond to make a 4-3 game.
It was time for Mets manager Terry Collins to go to the bullpen, and his relievers had a tough time throwing strikes. Right-hander Carlos Torres entered the game and walked Nate McLouth to load the bases. Then came left-hander Scott Rice, who walked Denard Span, sending LaRoche home to tie the score at 4.
The Mets would take the lead in the bottom of the eighth inning when Lagares led off the eighth inning against Tyler Clippard. Lagares swung at an 0-2 pitch and hit the ball over the wall in left-center to give New York the one-run lead.
But the Mets' bullpen couldn't hold the lead in the ninth. Closer Bobby Parnell was one out from victory, but with two outs and a runner on first, Danny Espinosa showed his patience from the left side of the plate. He saw eight pitches before drawing a walk to put runners on first and second.
"I was trying to stay comfortable and keep my at-bat at the pace I wanted it," Espinosa said. "I didn't want to feel rushed, and I didn't want to feel uncomfortable."
Span then doubled to left-center, scoring Desmond.
"When guys are in scoring position, you have to be ready to hit," Span said. "Even with my four-pitch walk, I was ready to hit every pitch. It was a good team effort today. It was one of the reasons why we were able to come back and win it."
The Nationals received a scare in the second inning. After Bryce Harper walked to lead off, Desmond hit a ground ball to third baseman David Wright, who threw to second baseman Young for the force. As Young was throwing to first, his knee hit the sliding Harper in the head. Harper was down for several minutes as Williams and head athletic trainer Lee Kuntz came to his aid.
Harper would get up under his own power and remain in the game, going 1-for-4.