Suter's three goals gave him five for the season -- all of which have come in the last four games for Minnesota, which won a second straight following a six-game skid.
Nino Niederreiter and Jason Zucker also scored.
Niklas Backstrom earned the win with 24 saves as the Wild improved to 7-0-0 all-time at home against the Capitals.
Mike Green scored twice for Washington, which stumbled to a fourth straight loss overall.
Marcus Johansson also scored and Braden Holtby stopped just six of the Wild's 11 shots.