Minnesota trailed by 12 in the fourth quarter, but closed within five heading into the final minute. Kevin Love had a chance to cut into that deficit, but his 3-pointer failed to go with 55 seconds left and the Timberwolves managed just two more points the rest of the way.
Lawson wrapped up the victory with four late free throws and was one eight Denver players in double figures.
Kevin Martin scored 29 points for Minnesota, hitting all 11 of his attempts from the foul line. The Timberwolves lost for the fifth time in six games.