Lee hit a 10-foot fallaway jumper over Spencer Dinwiddie to cap an electric Phoenix comeback in the season opener for both teams.
Cameron Johnson added 15 points, Mikal Bridges had 13 points and 11 rebounds and Lee scored 11 points off the bench.
Christian Wood added 25 points and eight rebounds in his Dallas debut while Dinwiddie added 15 points.
D'Angelo Russell added 20 points and Jaden McDaniels had 19 for Minnesota.
Santi Aldama (18 points, 11 rebounds) and John Konchar (12 points, 11 rebounds) each posted double-doubles while Jones had 15 points off the bench.