Phoenix never trailed but the Coyotes saw the Wild rally twice from one-goal deficits. Minnesota lost its fourth in a row.
The Wild forged a 2-2 tie on a wrist shot by Antti Miettinen with 4:58 remaining. It took Phoenix just 19 seconds to regain the lead.
Upshall took a feed from Keith Yandle and scored from a severe angle below the left circle.
Ilya Bryzgalov stopped 24 shots to get the victory.
Niklas Backstrom gave up three goals on 32 shots.