Werth, who signed a seven-year, $126 million contract in December, hit his first homer for the Nationals on his 42nd at-bat of the spring after driving in a run with a first-inning single.
Both Washington homers came off Detroit starter Rick Porcello, who gave up five runs and eight hits in five innings.
Jordan Zimmerman struck out six in five shutout innings for the Nationals.
"That guy overmatched us a little tonight, to be honest with you," said Tigers manager Jim Leyland. "We had some chances ... and we didn't get 'em in. Guys are out there (on base), that's why guys who drive 'em in get paid."
Brennan Boesch had three hits for the Tigers, who left six on base in the first four innings.
Zimmerman is 2-1 with a 2.70 earned run average in five spring starts.
"It took him 90 pitches, but that's because he's one of those guys who throws so well that guys are going to be fouling balls off and the count gets up there," said Washington manager Jim Riggleman. "He's making progress."