Both runners moved up on an infield out. Simon's second pitch to Roger Bernadina was low and inside and got away from catcher Devin Mesoraco, allowing Zimmerman to score.
Craig Stanman (1-0), who struck out the three batters he faced in the top of the 10th, got the win.
Washington loaded the bases with one out in the bottom of the ninth but the Reds turned a pitcher-catcher-first double play to end the threat.
The Nationals went up 2-0 in the fifth when Adam LaRoche delivered a bases-loaded, two-out single.