The Pacific Division championship was the first for the Coyotes in the 33-year history of the franchise and they needed a win on the final night of the regular season to get it.
Phoenix will take part in the playoffs for the third straight year, a streak that has followed an eight-year post-season absence. The Coyotes will face the Chicago Blackhawks in the first round.
Pyatt gave Phoenix a 2-0 lead with 6:03 to go in the second period and his other goal, coming with 5:36 left in the second, created a 3-1 advantage. Mikkel Boedker and Radim Vrbata also scored for the Coyotes.
Phoenix will be going into the playoffs with a hot goaltender. Smith has given up just two goals in his last five games and the only score he allowed against Minnesota came from Dany Heatley in the second period.
Niklas Backstrom gave up four goals on 28 shots to close out the season out of the playoffs for the fourth straight year.