Strasburg went seven innings, allowing two runs and six hits. He walked only one, but hit two batters, both of whom scored.
Both teams had their share of chances. The Reds were 2 for 24 with runners in scoring position, and the Nationals were 2 for 18.
The Reds were without first baseman Joey Votto (strained left quadriceps), who is rehabbing in Cincinnati, for the fourth straight game.
Trailing 2-0, Washington finally got to Leake in the seventh. Nate McLouth singled with one out and took second on a wild pitch. With two outs, Denard Span singled to right, scoring McLouth and ending Leake's night after 110 pitches.
The Reds used their legs to take a 1-0 lead in the fourth.
Frazier was hit by a pitch with one out and went to third on Brayan Pena's single. With Chris Heisey at the plate, Ramos blocked a pitch by Strasburg in the dirt and Pena broke for second. Frazier dashed home when Ramos threw to second and second baseman Espinosa's only play was on Pena, who was tagged out in a rundown.
The Reds made it 2-0 in the fifth. Zack Cozart was hit on the arm by a fastball by Strasburg. On a hit-and-run play, Hamilton singled him to third and Cozart scored on a single to center by Skip Schumaker.
NOTES: Williams said rookie RHP Blake Treinen will be called up from Triple-A Syracuse to make LHP Gio Gonzalez's scheduled start Thursday in Pittsburgh. Gonzalez (left shoulder inflammation) went on the 15-day DL Sunday. Treinen has made four appearances, including one start, for Washington. ... Williams said 1B Adam LaRoche (right quad strain) took pregame grounders for the first time since going on the DL on May 10. . Cincinnati's Jonny Cueto (4-2, 1.25) opposes Doug Fister (0-1, 4.76) on Tuesday.