Lawson's decisive running shot came only seconds after Milwaukee's Monta Ellis had put the Bucks ahead by one with a four-point play.
Lawson also dished out seven assists and Wilson Chandler provided 21 points for Denver, which clinched at least the fourth seed in the Western Conference and thus home court advantage in the first playoff round.
Ellis finished with 38 points on 14-of-25 shooting from the field for the Bucks, who hold the eighth seed in the East.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys