Strasburg was touched for three runs, all in the third when Travis d'Arnaud homered and Eric Young Jr. had a two-run double. The Nationals right-hander struck out seven and walked two in 5 2-3 innings.
''I got some good work in,'' Strasburg said. ''I came into spring wanting to work on another pitch (his slider), work on my time out of the stretch and controlling the run game and I feel like I got a lot more comfortable with that as the spring went on.''
While working on holding runners close at first base was a big part of Strasburg's spring, what batters should be more concerned about is his slider.
''It's just a natural pitch that I think can really help my game,'' Strasburg said. ''Based on what guys were doing off me in years past, it's kind of an equalizer.''
Mets starter Zack Wheeler lasted just 2 2-3 innings, allowing five runs on five hits, including Harper's homer. Wheeler threw 73 pitches, 40 in the third inning alone before he was removed.
Zimmerman homered off Mets closer Bobby Parnell in the eighth.
Harper appears to be full go after a pain-free spring, playing on his surgically repaired left leg.
''My knee feels great. That's all I really cared about,'' Harper said. ''The swing's going to be there, I know that. My outfield stuff's going to be there. My arm's going to be there. I'm just excited that I have no pain. I'm excited to go into the season.''
Mets: Wheeler was asked if he was being careful not to reveal too much of his game plan against a division rival.
''Honestly, I wasn't really that cautious,'' Wheeler said. ''It was just my fastball . I was just pulling off a little bit at the end. My off-speed was good. I was finishing through the pitch. Just a bad day. It's going to happen. It's good to get it out of the way in spring training.''
Because his next start won't be until next Thursday, Wheeler said he would throw two ''small bullpens'' between now and then to stay fresh.
Nationals: Right-hander Doug Fister (elbow inflammation) was scheduled to pitch against the Mets on Thursday, but will instead work in a minor league game. He is expected to throw between 60-65 pitches.
Mets: Left-hander Jonathon Niese (elbow inflammation) will throw 55-60 pitches in a minor league game Thursday. Niese is hoping to be ready to pitch for the Mets on April 6.
Following a discussion with Nationals manager Matt Williams in the eighth inning, the umpires decided to check the replay to see if Washington center fielder Denard Span had trapped a flyball by Andrew Brown.
The original call was that Span trapped the ball. As the play was being reviewed, Harper and several other Nationals walked back to the dugout, confident the call would be reversed in Washington's favor It was.
The Nationals announced before the game they released LHP Michael Gonzalez. Afterward, the club announced it had optioned right-hander Ryan Mattheus, lefty Xavier Cedeno and first base-outfielder Tyler Moore to Triple-A Syracuse. ... The team also released right-hander Chris Young and infielder Jamey Carroll ... Right-hander Aaron Barrett made the team as a reliever.