Peacock threw 1 2/3 innings of relief last week against the Los Angeles Dodgers, but this was his initial start in the majors after spending five seasons in the minors.
Washington scored both its runs on the third on RBI singles by Michael Morse and Jayson Werth. The runs were unearned courtesy of a fielding error by third baseman David Wright that extended the inning.
Peacock (1-0) allowed two hits and walked three over five innings in helping the Nationals win their fourth in a row and for the fifth time in six games.
Mike Pelfrey (7-12) suffered the hard-luck loss, giving up the two unearned runs on six hits in seven innings.