After being held to one run and one hit in seven innings by Chris Young, the Nationals and their experienced bench broke out against the Mets' shaky relievers for a 7-3 win in 11 innings.
Rodriguez hit a tiebreaking RBI single in the 11th inning and Laynce Nix followed with a three-run homer off the Mets' fifth reliever, Blaine Boyer (0-2), who was designated for assignment after the loss.
"If we can get into the sixth and seventh innings, we really feel good about our ballclub," Nationals manager Jim Riggleman said.
The Nationals actually left this one to the eighth, when an outfield gaffe was crucial to the outcome for the second game in a row.
Right fielder Lucas Duda misjudged Rodriguez's leadoff flyball. He sprinted toward center, but the ball sailed over his head. Rodriguez wound up with a leadoff double off D.J. Carrasco, who then walked pinch-hitter Matt Stairs with one out and gave up an RBI single to Ian Desmond before Rick Ankiel's grounder to second tied the game at 3.
"It's horrible, man," Carrasco said. "To just come in there and give the game away like that is very frustrating."
Duda was optioned to Triple-A Buffalo afterward and the Mets tried to bolster a bullpen that issued 11 walks and 10 hits in 11 innings this series by purchasing the contracts of pitchers Ryota Igarashi and Jason Isringhausen.
In the 11th, Rodriguez's hit got past second baseman Daniel Murphy, who pinch hit for Brad Emaus in the ninth after the Mets' bullpen blew a 3-1 lead in the eighth. Duda scooped up the ball, but his throw to the plate was inaccurate and pinch-runner Wilson Ramos scored easily.
"The route that was taken, I thought he was going to get there," Carrasco said. "I wasn't really worried because we had a two-run lead at the time. I twas the fact I couldn't control the cutter later on. That's what got me stuck."
Drew Storen (1-1) pitched a scoreless 10th for Washington, which salvaged a 3-3 road trip and took two of three from the Mets thanks to timely hitting from its bench players and five innings of scoreless relief.
The Nationals have won three out of four since dropping four of five to start the season.
"I think it's significant that we're playing good baseball more than anything," Nationals starter Jason Marquis said. "We started things off a bit sluggish. "
He was referring to the Nationals' season, but Young kept the Nats plenty quiet on Sunday, too.
"He got us to where we wanted to get to," Mets manager Terry Collins said. "He got us to the eighth inning and we couldn't hold it for him. It's a shame, but he pitched great."
Young looked right at home in Citi Field's wide-open spaces, getting 15 of his 21 outs on flyballs. The only groundout he allowed was Rodriguez's RBI to second base in the second inning.
Against Philadelphia last week, the big righty struck out seven and allowed one run in 5 1/3 innings in his Mets debut.
Davis got his 10th RBI, and Jose Reyes reached base in the first inning for the ninth straight game.
With the Mets' bullpen it wasn't enough.
"I guess you've got to convince them that they've got to get beat with somebody swinging the bat," Collins said. "This is the big leagues and they've got to be able to land some pitches. I'm not saying you're never going to walk somebody, but we're walking at too high a rate right now."
The night before, Jerry Hairston Jr. muffed a fly to left-center in the sixth inning, opening the door to a go-ahead triple by Ike Davis. On Sunday, the Mets repaid the favor. No Nationals pitcher has gone fewer than five innings yet this season, in nine games. Marquis retired nine straight between Reyes' single in the third and Willie Harris' in the fifth. Stairs drew his fourth walk in six ABs with Washington as a pinch-hitter. The Mets struck out 17 times one day after they whiffed 10 times. ... Washington 3B Ryan Zimmerman sat out. He aggravated an abdominal injury in Saturday night's game. Alex Cora played in his place. ... Carlos Beltran, who homered twice for New York the night before, pinch-hit in the ninth. His groundout to second ended the ninth. LaRoche left hurt in the 11th after reaching second base. Ramos, the backup catcher, ran for him. LaRoche said his left groin was tight.