Zimmerman (1-1), plagued by a lack of run support in his first three starts while compiling an ERA of 1.29, allowed only a solo homer to Orlando Hudson in the fifth. He helped his own cause with an RBI single during a two-run second that put the Nationals in front for good.
Washington improved the best record in the National League to 14-4 while the Padres have the worst mark in the league at 5-14.
The Nationals were protecting a 2-1 advantage before breaking loose for a four-run seventh. Adam LaRoche singled in a run in the inning, Jayson Werth drew a bases-loaded walk and Wilson Ramos had a two-run base hit.
Tom Gorzelanny worked the final three innings, which qualified him for his first save of the year.
The loss went to Joe Wieland (0-3), who allowed two runs on five hits and struck out four over six innings.
Washington has won the first two outings in a six-game road trip. After concluding its series against the Padres on Thursday, Washington moves on to Los Angeles.