The Nationals ace got off to a slow start. The Mets had runners on first and third with no outs in the first inning when Mike Baxter hit a sacrifice fly to left fielder Tyler Moore, scoring Jordany Valdespin to make it 1-0.
But Strasburg settled down, retiring seven of the next 10 hitters.
"I think I had little better fastball command," Strasburg said. "I was able to work it down underneath a little bit better. I threw a little bit more offspeed [pitches] and I felt pretty good."
With Rafael Montero on the mound for New York, Anthony Rendon doubled to right field, scoring Danny Espinosa and tying the score at 1 in the second inning. Making his Grapefruit League debut, Montero allowed just that run on three hits in two innings.
Right-hander Brandon Lyon was on the mound when Washington played small ball to take the lead an inning later. After he led off and walked in the third, Denard Span stole second and third base before scoring on a groundout by Jayson Werth.
However, Nationals left-handed Zach Duke couldn't hold on to the lead. An error by shortstop Ian Desmond allowed Travis d'Arnaud to reach second base after he singled with one out. d'Arnaud then scored on a double by Omar Quintanilla to make it 2-2.
Mets left-hander Josh Edgin was on the mound when the Nationals took a 3-2 lead in the fourth inning. Desmond scored on a groundout by Rendon, who leads the Nationals with five RBIs
The Mets kept fighting back against Yunesky Maya, as d'Arnaud scored on a single by Brian Bixler.
Elvin Ramirez was on the mound for the Mets when the Nats took a 4-3 lead in the sixth inning. With the bases loaded, Matt Skole walked, forcing home Chris Marrero.
Maya would allow the Mets to score the tying run in the next inning. He threw a wild pitch allowing Matt den Dekker to score.
Nationals reliever Ryan Mattheus was outstanding, pitching two shutout innings and striking out three batters.
It was the Nationals' second tie of the spring. Ask how he felt about the games ending in a tie, manager Davey Johnson said, "Awful, but at least we got 10 innings in. More guys got at-bats. Mattheus was outstanding. Strasburg was outstanding."
Up next: The Nationals return to Lake Buena Vista, Fla., on Friday night to play the Braves for the second time this week. The last time the two teams met was Tuesday with the Braves winning, 9-5. This time, right-hander Jordan Zimmermann will make his second start of the spring at 6:05 ET. He will throw about 60 pitches. In his last start against the Marlins, Zimmermann pitched three innings and allowed a run on two hits in a 2-2 tie.