Eovaldi allowed five runs and nine hits in three innings en route to a 9-2 loss to Washington.
"We were hoping for another good pitching performance like the one (from Jose Fernandez) Friday night," Miami manager Mike Redmond said.
"It didn't work out that way and Washington showed that it can do a lot of damage."
Eovaldi (3-6) had his shortest outing of the season.
"I was battling out there; trying to limit the damage," Eovaldi said. "You just have to have short-term memory and forget this one. You try to learn from it and move on."
Redmond had a hunch early on that Eovaldi's night might be a short one.
"They were squaring him up pretty good," Redmond said. "You could see that it wasn't going to be his night. We got out of the game early."
Ryan Zimmerman homered twice and drove in three runs for the Nationals.
Jayson Werth and Anthony Rendon had three hits apiece as the Nationals won for the third time in four games to remain on the fringe of the NL wild-card race. Tanner Roark (5-0) pitched six scoreless innings in his first start of the season.
Adeiny Hechavarria and Jeff Mathis each drove in a run for Miami. Christian Yelich, who extended his hitting streak to eight games with his 14th multi-hit game, had two hits and scored a run.
Washington got off to a fast start behind Zimmerman, who drove a 1-2 pitch over the wall in center in the first to give the Nationals a 2-0 lead.
Zimmerman's 18th homer came after Denard Span reached on a leadoff single to extend his career-high hitting streak to 18 games.
"It's a big park. You just hit the ball hard and hopefully good things will happen," Zimmerman said. "After two home runs you're feeling pretty good ... a decent night."
Zimmerman belted Eovaldi's first pitch of the third over the wall in right for his 12th career multihomer game. Washington added two more runs in the inning on Wilson Ramos' two-run single.
Span added a sacrifice fly in the sixth and Adam LaRoche doubled home a run in the seventh, helping the Nationals improve to 10-4 against the Marlins this season.
Roark struck out four and walked none. He was 4-0 with a 1.19 ERA in nine relief appearances before joining the rotation.
"We got a couple runs early and that takes a lot of weight off your shoulders," Roark said. "I keep going at guys, keep attacking, (I'm thinking) don't give into anybody."
Washington manager Davey Johnson was thrilled with Roark's performance in combination with the club's ability to put up some good numbers offensively.
"The story really was Roark. He really pitched a great game," Johnson said. "It's one thing to have great stuff, but he has great command. He throws it like Satchel Paige."
Tyler Moore went 2 for 5 with two RBIs after replacing Bryce Harper in Washington's lineup. Harper was scratched after what Johnson said after the game was inflammation in his hip.
"He's going to go to see the doctor tomorrow, figure out what it is, treat it, and he'll meet us in New York, hopefully," Johnson said.
Marlins' slugger Giancarlo Stanton is also scheduled to be evaluated Sunday after leaving the game as a precautionary measure in the seventh inning with a sore ankle. He is listed day to day.
Miami got on the board in the seventh on consecutive RBI singles by Hechavarria and Mathis.
NOTES: Ryan Zimmerman has hit 15 of his 19 home runs on the road...Span was back in the leadoff spot after taking batting practice and feeling no discomfort from the on-and-off tightness this week in his right groin. ... NL Rookie of the Year candidate Jose Fernandez will not have an innings limit when he pitches in his final game of the season Wednesday against Atlanta. Manager Mike Redmond said Fernandez won't be pulled just because he has reached the club's previously stated 170-inning cap. He has 165 2-3 innings...Chris Coghlan continues to excel at Marlins Park. He has hits in eight straight games, and has reached base in 12 consecutive games, in Miami.