Denver owned a 22-point lead in the early stages of the second half, but Minnesota came back to get within two in the final minute. J.J. Barea had a chance to tie it for the Timberwolves, but he missed a jumper with 23 seconds to go and Lawson grabbed the rebound.
Lawson hit two free throws to put Denver ahead by four and he converted two more after Minnesota's Martell Webster misfired on a 3-point attempt.
Lawson finished with 24 points and Arron Afflalo had 21 for the Nuggets, who moved into a tie with Dallas for the seventh and eighth spots in the Western Conference. Utah is in ninth, 1 1/2 games behind Denver and Dallas.
Anthony Randolph had 28 points for the Timberwolves and Derrick Williams had 27. Minnesota has lost seven in a row, its longest such streak of the season.