Jackson (1-0) needed just 85 pitches to rack up his fifth career complete game. The right-hander yielded just one walk and struck out nine in the dominating performance, handing the Nationals a fifth straight win.
Homer Bailey (0-2) took the loss for the Reds, allowing three runs on seven hits over six frames. He walked four and struck out three.
Drew Stubbs provided the only RBI for Cincinnati, which lost for the sixth time in nine games to start the season.