Murray took advantage of the injury absence of Bucks star Giannis Antetokounmpo to lead the scoring for Denver, who improved to 43-21 with the win on Monday, AFP reported.
Murray was one of six Denver players to reach double figures, with Paul Millsap adding 20 points and 10 rebounds while Jerami Grant added 19 off the bench.
The injury-hit Bucks, however, struggled to match Denver's offensive depth, with point guard Sterling Brown (16 points) and center Robin Lopez the only starters to make double figures.
Kyle Korver led the scoring for the Bucks with 23 points from the bench including five three-pointers.
Milwaukee was without reigning MVP Antetokounmpo, who injured his left knee during Friday's defeat to the Los Angeles Lakers at the STAPLES Center.
The Greek star also missed Milwaukee's defeat to the Phoenix Suns on Sunday.
The defeat leaves Bucks with a mountain to climb if they are to become only the third team in history to post a 70-win regular season.
The Bucks, who have already qualified for the playoffs, must now win their remaining 17 games to reach the magic 70-win mark.
Denver, meanwhile, has boosted its chances of claiming the second seed spot in the Western Conference to join the Los Angeles Clippers on 43 wins.
The Los Angeles Lakers lead the West by 6.5 games with a 49-13 record.
Elsewhere on Monday, the NBA champion Toronto Raptors held on to secure a nail-biting 101-92 win over Utah Jazz in Salt Lake City.
Cameroon international Pascal Siakam and Serge Ibaka led the Raptors' offensive effort with 27 points each, while Kyle Lowry had 21 points with five rebounds and seven assists.
Siakam also had a big game defensively, hauling down 11 rebounds and grabbing five turnovers. Joe Ingles led Utah with 20 points.
Toronto remains on course for second spot in the East behind Milwaukee, with 46 wins and 18 defeats. Utah is fourth in the West behind the Lakers, Clippers and Nuggets.
In Monday's other game, the Atlanta Hawks delivered a rare victory to their long-suffering fans with a 143-138 overtime win over Charlotte.
Atlanta, which is bottom of the Eastern Conference with 19 wins and 46 defeats, claimed victory after 31 points from Trae Young and 28 points from John Collins.