Gortat laid in the tying basket in the closing seconds of regulation and Johnson chalked up nine rebounds in the win, which ended the Suns' three-game losing streak.
Derrick Williams led Minnesota with 21 points and 12 rebounds. Niko Pekovic also tallied a dozen rebounds and scored 18 points to round out the double-double.
The T-Wolves outscored the Suns 26-19 in the fourth quarter and were ahead 77-75 when Gortat tied it up with 13.6 seconds to play. Gortat scored three of Phoenix's six points in overtime.