Maholm (3-0), who hasn't allowed a run in 20 1/3 innings over three starts to begin the season, held the Nationals scoreless on four hits. The left-hander issued only one walk while striking out seven.
Simmons' clout in the third inning gave the Braves a seven-run lead and they cruised to their 11th win in 12 games beginning the 2013 campaign.
Nats stater Gio Gonzalez (1-1) was roughed up for seven runs on seven hits over five frames.
Kurt Suzuki had two singles for Washington.