Strasburg mostly sailed through the Tigers' lineup, throwing 46 of his 66 pitches for strikes. He gave up three hits, walked one and struck out five.
The big right-hander only retired the side in order once but induced two double plays and saw a runner caught stealing, a good sign for a pitcher who has worked to hold runners more effectively. He got in one jam, putting runners at second and third with one out in the fifth, but struck out Nick Castellanos and retired Trevor Crowe on a groundout.
"I'm just trying to go out there and commit to every pitch and see what happens," Strasburg said.
Scherzer, who will yield Detroit's Opening Day start to Justin Verlander, gave up five runs on seven hits in 5 2/3 innings, although he struck out eight without a walk.
The Nats struck against the reigning American League Cy Young Award winner in the third, after Danny Espinosa led off with a single. Following a Strasburg sacrifice bunt, Denard Span hit a grounder up the middle that took shortstop Danny Worth into center field and allowed Espinosa to score, narrowly avoiding a tag from catcher Alex Avila. One batter later, Desmond launched a pitch well over the wall in left-center field for a two-run shot.
"Overall, I threw the ball pretty well. I just didn't execute pitches," said Scherzer. "The shape of all my pitches, the break, it's all there. Now I'm just trying to catch up on the execution. But to be able to keep going out and not walk anybody in basically six innings, that's a really good sign."
Tigers left fielder Tyler Collins saved another homer in the fifth, reaching over the wall to pull back a long drive from pinch-hitter Chris Snyder. Scherzer exited in the sixth after giving up an RBI triple to Ryan Zimmerman and an RBI single to Jose Lobaton.
Detroit pushed across a run in the sixth against Drew Storen on an RBI single by Victor Martinez.
Lobaton added a two-run double after Anthony Rendon's RBI single during a three-run eighth against Tigers reliever Blaine Hardy.
Up next: The Nats will travel to Jupiter, Fla., on Friday to square off against the Cardinals at Roger Dean Stadium. The game will be carried on MLB.TV at 1:05 p.m. ET. Left-hander Gio Gonzalez will make his fourth start of the spring after giving up three runs in 8 2/3 innings over his first three. Righties Tyler Clippard and Aaron Barrett are scheduled to follow as Washington faces St. Louis ace Adam Wainwright.