"It's been really eating away at me for the last few weeks. I haven't really been doing my job," Gee said. "I'm just happy to finally contribute to a win."
Following a pair of poor starts, Gee (1-3) used an effective changeup to toss three-hit ball over 5 2/3 innings. It was his first win since his 2012 season was cut short in July by surgery to replace a damaged artery in his right shoulder.
"I think he needed it bad. I think it's a great confidence builder for him," Mets manager Terry Collins said. "He needed this just psychologically that he's going to be OK. ... I think it's huge for him."
New York also got a strong effort from its struggling bullpen, which entered with the highest ERA in the majors at 5.47. Buck hit a drive into the second deck at Citi Field and Mike Baxter added a sacrifice fly as the Mets ran up Jordan Zimmermann's pitch count enough to deal the right-hander his first loss of the year.
The Mets, 4-14 against the Nationals last year, have won their first three series at home for the first time since 2006.
"They're a great team and to come out and take two of three from them is big," Gee said.
Slick defensive plays by Buck behind the plate and Ruben Tejada at shortstop gave the Mets a boost. Meanwhile, Washington committed three errors -- though none proved costly.
The Nationals tried to rally in the eighth when pinch hitter Steve Lombardozzi led off with a single and Denard Span walked against 31-year-old rookie Scott Rice. But with the meat of the order coming up, Jayson Werth grounded into a double play on a 3-0 sinker.
"I was looking to pull something. I even moved up on the plate. He threw like seven straight balls in a row, felt like he was going to groove one there," Werth said. "I felt like I let the guys down, that's the bottom line.
"I got caught up in the moment. Looking back, I was trying to do too much. I was trying to win the game right there. The situation got the best of me," he added. "It's probably one of the dumber things I've done on the field for a while. I feel like I pretty much blew it."
Collins and Buck acknowledged they were surprised to see Werth swing. David Wright even said the Mets "got lucky on that one."
Rice, however, had an inkling that Werth might be hacking.
"Jayson Werth gets paid a lot of money to drive in runs," Rice said. "I was able to make a pitch when it mattered and get out of it."
The left-hander then struck out Bryce Harper, who homered twice and doubled Saturday in Washington's 7-6 victory.
With the Mets almost desperate for a solid start from someone other than Harvey (4-0, 0.93 ERA) or Jonathon Niese, Gee came through.
"If we want to be competitive in our division, we can't just have two starters throwing well. We need to have three or four," Buck said. "So it's huge for (Gee) to get back on track like that."
The right-hander struck out six and did not walk a batter until issuing three free passes in the sixth. But he got some help when Buck made a tough, backhand pickup of a breaking ball in the dirt and threw out Span trying to scamper to second.
"Eyes were shut," Buck said with a grin.
"We just passed the baton today. Everybody went out there and did their job," Hawkins said.
Coming off a complete game at Miami, Zimmermann (3-1) threw 96 pitches in five innings. He allowed two hits and three walks.
"I fell behind guys, didn't throw a lot of first-pitch strikes," Zimmermann said. "Without first-pitch strikes, you have to work a little harder."
Anthony Rendon went hitless with two strikeouts for Washington and committed an error in his major league debut. Selected sixth overall in the 2011 amateur draft out of Rice, he was called up from Double-A Harrisburg to fill in for injured third baseman Ryan Zimmerman.
Before the game, Rendon said his parents tried to fly in from Houston for his debut -- but airline trouble left them without seats even though they thought they had booked their reservation. He said his parents plan to be in Washington to see him play when the Nationals return home Monday to face St. Louis.
Buck launched a drive to left-center leading off the second, giving him 22 RBIs in his first three weeks with the Mets after arriving in the trade that sent NL Cy Young Award winner R.A. Dickey to Toronto.
"I don't know where we'd be without John Buck," Collins said.
A leadoff walk to Wright in the fourth and Ike Davis' hit-and-run single set up Baxter's sacrifice fly.
Zimmerman was placed on the 15-day DL, retroactive to April 18, with a strained left hamstring. ... Nationals reliever Zach Duke struck out four in two scoreless innings. ... The Mets recalled LHP Rob Carson from Triple-A Las Vegas and designated LHP Aaron Laffey for assignment. ... New York's first shutout of the season was the third blanking of Washington this year. ... The Mets had not won a series against the Nationals was in September 2011 at Washington.