Kearns, who had two hits, leads the Marlins with nine RBIs this spring. The veteran is a non-roster invitee who is battling to earn a job as a right-handed bat off Miami's bench.
Ricky Nolasco worked 6 1/3 innings -- the longest outing for a Marlins starter this spring -- allowing one run with four strikeouts. The right-hander effectively pounded the zone, throwing 60 of his 83 pitches for strikes.
"He's heading the right way heading into the season," Marlins manager Ozzie Guillen said of Nolasco. "He's got a lot of movement, throwing a lot of strikes."
Gio Gonzalez, the Nationals' No. 2 starter, settled down after a rough first inning. The left-hander, who grew up in Miami, gave up three runs on seven hits with six strikeouts in five innings. He threw 81 pitches, with 53 strikes, while walking one.
After Nolasco worked through the first inning on four pitches, the Marlins responded with three quick runs off Gonzalez.
Jose Reyes opened the first with an infield single, and he stole second. With one out, Hanley Ramirez walked and Gaby Sanchez delivered an RBI single. Kearns made it 3-0 with a two-out, two-run double to left.
Nolasco held the Nationals scoreless until Roger Bernadina lifted an RBI single to center in the sixth. Mark DeRosa, who singled to open the inning, scored from second.
Nolasco's afternoon ended in the seventh after he retired Ian Desmond on a lineout to third.
Up next: Miami is on the road on Wednesday, taking on Houston in Kissimmee. Carlos Zambrano, the team's No. 4 starter, will take the mound, and the aim is to get the right-hander up to about 90 pitches. Aaron Rowand, Kearns, Sanchez, Emilio Bonifacio, John Buck, Bryan Petersen, Nick Green and Chis Coghlan are position players making the trip. Lucas Harrell will get the start for Houston.