Bryan De La Cruz had his first career four-hit game with a homer, two doubles and a single for Miami.
The 27-year-old Alcantara (14-8) allowed Joey Meneses' home run in the first and little else.
''When the hitters are so aggressive you have to take advantage of the over-swing,'' Alcantara said. ''After that first inning I just wanted to finish the game. That's my mentality all the time.''
In his 13th start of at least eight innings this season, the All-Star righty gave up three hits, walked one and hit a batter.
After striking out the side in a perfect eighth, Alcantara was lifted at 99 pitches. A few boos from the crowd of 16,099 were heard when Dylan Floro entered to pitch the ninth. Floro closed for his seventh save.
''It's one of those you've piled up enough innings on him, he hasn't had any kind of struggles and it's going to be hard to take him out,'' Marlins manager Don Mattingly said. ''To let him go out with 10, 12, 15 (additional pitches) whatever it ends up being, it doesn't seem to make sense where we are now.''
Alcantara, who has thrown a major league-leading 220 2/3 innings, accepted the decision but wanted to string two consecutive complete games after his seven-hitter at Washington on Sunday.
''It's always hard because I never want to leave the game,'' Alcantara said. ''It doesn't matter how many innings I throw.''
JJ Bleday's two-run single in the first put the Marlins ahead 2-1. The sinking line drive to right-center fell between outfielders Victor Robles and Lane Thomas, scoring Brian Anderson and Garrett Cooper.
De La Cruz connected against Erick Fedde (6-11) to lead off the fourth. It was his 11th homer of the season and fourth since being recalled from Triple-A on Sept. 6.
''When I put my mind on something, I achieve it,'' De La Cruz said. ''My batting practice today was really good. I was feeling it.''
The Marlins added a run in the sixth on Miguel Rojas' two-out RBI double, ending Fedde's outing.
Fedde gave up four runs and nine hits, walked one and struck out four. He had a 4-1 career record and 2.24 ERA against Miami before his start Saturday.
The Nationals struck quickly against Alcantara with Meneses' drivet in the first. Meneses drove Alcantara's sinker over the wall in right for his 11th homer.
''Joey got us going right away,'' Nationals manager Dave Martinez said. ''He drove a pretty good pitch to right field. He was ready to hit.''
PLAYING IT SAFE
De La Cruz briefly thought of stretching his second double to left in the eighth into a triple and becoming the first Marlins player to ever hit for the cycle. But De La Cruz, who didn't know of the club's elusive feat until informed by Rojas, played it safe and remained at second when left fielder Alex Call quickly retrieved his drive to the wall.
''It was going to look too obvious,'' De La Cruz said. ''I wasn't going to risk it going to third so I settled for the double.''
With loanDepot park serving as host of all three rounds of the World Baseball Classic, a mural depicting the event next spring was unveiled before the game.
Nationals: LHP Patrick Corbin (back spasms) will not make his next start after he didn't throw his bullpen Saturday. ... DH Nelson Cruz (left eye inflammation) missed his ninth straight game.
RHP Anibal Sanchez (2-6, 4.40) will start the series finale for the Nationals on Sunday and the Marlins will go with RHP Edward Cabrera (6-3, 2.91).
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