Matsuzaka allowed one run and three hits in 3 2-3 innings with four strikeouts and no walks. He is competing with John Lannan and Jenrry Mejia and said through an interpreter he has been ''preparing, expecting myself to be in that position.''
Denard Span doubled leading off the first, stole third and scored on Bryce Harper's grounder for the only runn off Dice-K.
''I'm not the one that makes the decisions, so it's hard to say, but so far I think I've pitched pretty well,'' Matzusaka said. ''I'm pretty satisfied with what I've done so far.''
Detwiler also gave up one run and three hits in 3 2-3 innings. He struck out two.
''I think the biggest thing is it's making the fastball better because they can't just sit there and sit on the fastball the whole time,'' Detwiler said. ''I'm seeing it more when I get in good counts. When I'm ahead in the count, I can do a lot more than being behind in the count. Then, we're back to square one throwing a lot of fastballs because the confidence isn't completely there in the offspeed.''
Detwiler is competing with Taylor Jordan and Tanner Roark for the fifth spot.
''If I go out there and throw well, and feel good coming out of it, then I think I'll have a good chance at whatever I'm supposed to do,'' he said. ''If I don't, then I don't deserve it.''
Washington's Brock Peterson hit a three-run homer. Kirk Nieuwenhuis had three RBIs and Josh Satin drove in two for New York.
Nationals closer Rafael Soriano, roughed up in his first two spring training outings, pitched a scoreless inning and struck out David Wright.
Mets prospect Noah Syndergaard struck out five, walked two and gave up three runs and two hits in 3 2-3 innings.
Nationals RHP Doug Fister (elbow inflammation) reported feeling a little ''tight'' after throwing on flat ground for the third consecutive day Thursday. He is still scheduled to throw a bullpen session Friday, then be evaluated.
Williams theorized the tightness could be attributed to three consecutive days of throwing and the weather conditions.
''It's a cold, windy day out there, so we're not putting too much into that,'' Williams said.
Ryan Zimmerman is not expected to play until Saturday because of shoulder and body tightness. Williams wasn't concerned about the injury being serious.
Left fielder Bryce Harper started Thursday's game, but is dealing with a chest cold and will be off Friday and evaluated for Saturday. Shortstop Ian Desmond, already bothered by an injured finger, was also feeling ill and was sent home Thursday.
New York 1B Ike Davis (calf muscles) and OF Lucas Duda (hamstring) are still day to day. Mets manager Terry Collins said if Duda did anything Friday, it would be on a back field.
NATIONALS MAKE MORE CUTS
The Nationals optioned outfielder Michael Taylor and left-hander Matt Purke to Double-A Harrisburg. The team also reassigned right-handers Clay Hensley, Josh Roenicke and Daniel Stange to minor league camp along with left-hander Danny Rosenbaum.