The winning goal came just after New York's John Mitchell won a face off in Capital territory. The puck came out to Staal who skated toward the center of the rink before firing a shot past Braden Holtby.
Staal's goal was the Rangers' second power-play goal scored on Joel Ward's double minor penalty for a high stick. Brad Richards scored the first with 6.6 seconds left in regulation. Prior to Richards' goal, the Rangers had scored on just two of their 16 power-play opportunities in the series.
The Rangers now lead the best-of-seven series 3-2. The Capitals were just seconds away from stealing a game on the road, but will now head back home needing a win to avoid elimination.