New York tied the season series at 7-7 and dropped Washington to 7 1/2 games behind Cincinnati for the second National League Wild Card spot.
"We're playing without our best player, our best pitcher and our best reliever, so it just shows us what we can be at full strength," third baseman Josh Satin said, referring to disabled-list residents David Wright, Matt Harvey and Bobby Parnell. "I think the sky's the limit with this team. ... We have a bunch of guys who are playing hard, and it's always nice to beat the division rival when they're playing for something, kind of knock them out."
The only bad news for the Mets was that first baseman Ike Davis strained his right oblique hitting a sacrifice fly in the third inning and left the game. His season is likely finished, but just about everything else went the Mets' way.
Eric Young Jr., Daniel Murphy, Satin and Juan Lagares all notched three hits for the Mets, who collected 17 to set a season high for a nine-inning game. New York has scored 11 runs in two of its past three games -- all wins -- after managing 13 over its previous seven.
Wheeler (7-3) was in control during his 14th big league start. The right-hander notched his fifth straight quality start, holding Washington to two runs on five hits over 6 2/3 innings, with a hit batter, one walk and three strikeouts. He moved his ERA over those five games to 2.51 and his road ERA to 2.19 in eight outings.
"He's throwing strikes. That's what we're seeing," Mets manager Terry Collins said. "He's not trying to strike people out, which is what everybody thought, with the great arm he had, people were looking for that. I think when he got up here, he thought he had to do that. I think while he was here, he said, 'Hey, look, I don't have to. I can get outs if I pitch to contact and stay in games longer.'"
The Nationals didn't pick up their first hit until relief pitcher Tanner Roark bounced an infield single to the right of Murphy at second base with two outs in the third. By that point, Wheeler already had an eight-run lead.
The Mets hit the ball in the right spots to get on the board against Haren in the second. With one out, Travis d'Arnaud ripped a single just past third baseman Ryan Zimmerman, and Lagares pushed a seeing-eye single through the right side. One out later, Omar Quintanilla's liner into right-center narrowly eluded a diving Denard Span, and New York grabbed a 2-0 lead.
More well-placed hits and some aggressive baserunning helped in the third, when the Mets equaled their highest-scoring inning this season and sent 11 batters to the plate. Young stole second after a leadoff single and scored on Murphy's single up the middle on a 3-0 pitch. Murphy then took off for second on the next pitch, cruising to third when Satin singled to left, and then scored on Davis' sac fly.
Satin was later thrown out at home on a single by Lagares, but Matt den Dekker came through with his first Major League hit and RBI on a soft single over shortstop that chased Haren. Roark walked Quintanilla to load the bases and Wheeler to force home a run before Young capped the big inning with a two-run single.
"It was one of those days for [Haren] where it seemed like every mistake he made, we were able to capitalize," Satin said. "Once the momentum starts going in our favor, it gets a lot easier to hit when other guys are hitting."
Wheeler lost his shutout in the sixth after loading the bases with one out on a hit batter, a single and a walk. Jayson Werth hit a sacrifice fly, and Ian Desmond lifted a broken-bat RBI single just over shortstop, but after a mound visit, Wheeler got Adam LaRoche to line out to center field to escape further damage.
Wheeler had said recently that he was feeling some fatigue, but with 88 pitches up to that point, he told Collins he wanted to go out for the seventh.
"Then stop telling everyone you're tired, and you will go back out there," Collins said with a smile. "But what that shows you is that no matter what he says, this guy competes."
"My [velocity's] not up, so obviously I'm a little tired," said Wheeler, who still averaged better than 95 mph with his fastball. "But once you get out there and get going, you don't even know about it. I stayed out there for the seventh, and still felt as strong as I did in the first. Once you go out there and your adrenaline going, you don't even feel it."
Wheeler exited with two outs in the seventh, after Anthony Rendon hit his 99th pitch for a single to right field. The Mets tacked on three more runs in the eighth.