In his fifth and final appearance of the spring, Matz left with a 4-1 lead. The left-hander didn't allow a hit until Clint Robinson's two-out homer in the fourth.
''I felt good and was attacking the zone early. In the last inning I was running out of gas. It was a really humid day,'' said Matz, who struck out five and walked four.
Wright hit his first home run, a solo drive in the first off Yusmeiro Petit. In the second, Neil Walker tripled and Conforto homered.
Wright added an RBI single in the fifth.
''Right-center field is a power spot. I was just glad to see him get in there and get four (at-bats),'' manager Terry Collins said.
Matt den Dekker had an RBI single in Washington's two-run eighth.
Shortstop Asdrubal Cabrera was scheduled to play for New York but instead played in a minor league game on a back field. He stayed in for four innings and got three hits.
Cabrera strained a knee tendon on March 10. His rehab had him on schedule to be ready for opening day in Kansas City next Sunday.
Cabrera doubled and singled in a minor league game Saturday as the designated hitter. The Mets newcomer is 7 for 13 in three minor league games since the injury.
''He said he wasn't ready for the defensive side. He said he hadn't seen any game groundballs,'' Collins said.
Nationals: Petit, likely will be the club's long man in relief, yielded a pair of homers among the eight hits New York had against him in 4 1/3 innings.
Mets: Matz is scheduled to make a final exhibition start against the Chicago Cubs in Las Vegas on Friday. Collins said he may be able to use Matz in the second game in Kansas City next Tuesday, saying: ''He is (a possibility).''
Mets: OF Yoenis Cespedes (shoulder), 1B Lucas Duda (neck) and Conforto (back) all returned to the lineup after minor injuries earlier in the week. The three combined to go 1-for-10 with a homer and two RBIs.
Nationals: RHP Stephen Strasburg (2-0, 3.21) will start Monday in Viera against the Miami Marlins.
Mets: RHP Bartolo Colon (1-1, 6.62) gets the start as New York travels to Jupiter to face St. Louis and RHP Carlos Martinez (0-1, 2.79).
HAPPY TO HAVE HIM
Nationals OF Michael Taylor's strong spring (20 for 44) could force the club to make a tough decision on his playing time in the outfield, which already features National League MVP Bryce Harper, leadoff hitter Ben Revere and $21 million man Jayson Werth.
Bench coach Chris Speier served as manager of the traveling split squad while manager Dusty Baker stayed in Viera to watch the home split squad against Atlanta.
''He's done everything,'' Speier said of Taylor. ''People in the organization have said he's a comer and the real deal. He's another one that's going to make it really tough on Dusty. You get a guy like that, how do you keep him out of the lineup?
''I'm glad I'm only doing this for a day. The other good thing is Taylor's on my team.''