Harper, the 2012 National League Rookie of the Year, had a two-run double in the third inning and added a two-run single in the fifth off Marlins starter Wade LeBlanc.
Nationals right-hander Chris Young kept Miami off-stride for five innings, yielding two hits and no runs. The right-hander, throwing in the mid-80s, struck out two. He threw 64 pitches, with 42 strikes.
"There's still work to be done, progress to be made, but it's an improvement," Young said. "That's the way spring's supposed to go. You're supposed to get a little bit better each time. I feel like I've made strides. Not where I want to be yet, but getting closer and feeling good. That's the most important part."
LeBlanc, a frontrunner to be Miami's fourth starter, entered Wednesday without allowing a run in nine Grapefruit League innings. The string reached 11 innings before Washington pushed three runs across in the third inning.
In five innings, LeBlanc, who also was throwing in the mid-to-upper 80s, gave up six runs on seven hits in five innings. Exiting after 84 pitches, LeBlanc finished up with some more pitches in the bullpen.
Washington moved on top in the third inning.
Kurt Suzuki started a string of three-straight singles to open the inning. Young reached on a bunt single on a play LeBlanc attempted to make with a diving catch. Denard Span bounced a single into right field, filling the bases. Jayson Werth lifted a sacrifice fly to right, and Harper drove in two with a double to left-center.
Before Wednesday, LeBlanc did give up three runs (two earned) in 2 2/3 innings in an exhibition against Team Venezuela, which was preparing for the World Baseball Classic.
In the fifth inning, the Nationals did more damage with another three-run frame. Again, Harper had the big hit, a two-run single. Ryan Zimmerman's sacrifice fly to right padded the lead to 6-0.
A couple of walks to open the fifth -- including a leadoff walk to Young -- set up the big inning.
In the sixth inning, Miami got back into the game, stringing together five-straight two-out hits off Zach Duke.
Giancarlo Stanton had an RBI double, and Greg Dobbs chipped in with a run-scoring single. Rob Brantly had a two-run double.
Up next: Washington stays out on the road Thursday, with a game against the Braves under the lights in Orlando at 6:05 p.m. ET. Roger Bernadina will be back after nearly a month at the World Baseball Classic, and right-hander Dan Haren will be on the hill after a rough outing during his last start. The game can be seen online on MLB.TV.