Lucas Duda, out this spring because of a strain on his left side, made his spring debut for the Mets. Normally a first baseman, he was the designated hitter and went 1 for 4.
Wright hit his first homer in exhibition play, a three-run shot off Tanner Roark that cleared the high wall above the 410-foot mark in center field.
Cuddyer and Mayberry each hit their second home run. Kevin Plawecki had a three-run double for the Mets and Reuben Tejada drove in two runs.
Ian Stewart homered for the Nationals.
"It's always fun to hit a home run," Wright said. "It's good, especially this early in spring, to make good contact and get good results. When you see the results from work, it's fulfilling and nice," said Wright.
The seven-time All-Star third baseman hit a career-low eight homers last season, marking the only time in his 11-year career he has hit fewer than 10 homers.
Mets manager Terry Collins said the homers will come for Wright.
"That ball was mashed," Collins said. "If he works on hitting the ball hard, those things happen. He's got that kind of power. It was good for him today to know he can still hit a ball like that."
Ian Stewart hit Washington's lone home run.
The Mets rolled up 13 runs for the second straight day, beating the Braves 13-2 Friday.
Roark, who may be destined for the bullpen with the signing of Max Scherzer, was facing a what was close to the Mets regular lineup — other than Duda, who made his first appearance this spring because of a left intercostal strain. He served as the designated hitter and went 1 for 4.
"I made one bad pitch, didn't get it inside and left it right down the middle (to Wright). I felt good and strong; it was just that one bad pitch," said Roark, a 15-game winner in 2014.
Duda lined a single off Dan Uggla's glove in the third.
"It's nice to get a hit, but for the most part I was trying to see the ball a bit and get my timing down," said Duda, who is slated to play first base Sunday in Port Charlotte.
Nationals: Roark allowed four hits and four earned runs in the third inning. The output ballooned his ERA to 14.29, but he said he felt fine and strong and was able to locate most of his pitches.
Mets: Prospect Tyler Pill, a replacement for RHP Zack Wheeler, tossed 2 1-3 innings of scoreless work, allowing just a pair of baserunners. Pill spent most of 2014 at Double-A Binghamton and was 9-5 with a 3.83 ERA.
Nationals: Washington begins a home-and-home with Houston on Sunday in Kissimmee. Scherzer starts for the Nationals against Astros RHP Asher Wojciechowski.
Mets: New York travels to Florida's West Coast for games on Sunday and Monday. RHP Bartolo Colon is scheduled to start the first one against Tampa Bay in Port Charlotte; RHP Matt Harvey pitches Monday against Boston in Fort Myers.
Nationals: OF Nate McLouth (shoulder) was a late scratch from Washington's lineup after being penciled in as the leadoff hitter. ... INF Anthony Rendon, injured Monday while diving for a groundball, will be shut down from baseball activity for a few days. The infielder hurt his left knee on the play and had pain following the game. He was expected to play Wednesday, but an MRI revealed a slight sprain in his MCL. ... RHP Drew Storen (minor left hand surgery) will miss a few days but is still on track for the regular season. ... OF Denard Span (abdominal surgery) is likely out until May, while INF Yuniel Escobar (oblique strain) is also out.
Mets: Wheeler, scratched from Saturday's start because of a blister and a sore elbow, said he feels all right and that he would be day to day. He said he has dealt with the elbow pain occasionally throughout his career and that it was not affecting him too much, adding, "It's spring training. You don't want to push yourself in spring training." ... RHP Vic Black had an MRI Friday on his right shoulder after having one in January. The procedure revealed weakness but no structural damage. He will rest for two days. "Just some soreness and fatigue. The achiness has been off and on through the winter," Black said.