Murray made 9 of 18 shots and a trio of 3-pointers in the 101-94 triumph Thursday at Staples Center in Los Angeles.
"Coach put the ball in my hands and trusted me," Murray told reporters. "I just went out there and made a play."
The Clippers, who entered the game with wins in six of their last seven games, shot 41.2% from the floor and made 29.4% of their shots from 3-point range.
Nuggets guard Will Barton made a floater 34 seconds into the game and Denver never lost that advantage.
The Nuggets later added an 11-0 run to push their lead to 20-9 midway through the first quarter. Barton scored 10 points in the first 12 minutes to give the Nuggets an early 31-20 lead.
Murray then got hot with 11 points in the second quarter to help the Nuggets take a 62-49 lead at the half. The Clippers outscored the Nuggets 45-39 down the stretch, but could not close the gap.
NBA MVP contender Nikola Jokic scored 14 points and had seven assists and seven rebounds for the Nuggets. New Nuggets forward Aaron Gordon chipped in 14 points, six assists and six rebounds. Michael Porter Jr. had 20 points in the win.
Kawhi Leonard paced the Clippers with a game-high 24 points. The All-Star forward also had 12 rebounds, four assists and two steals. Terance Mann chipped in 18 points off the Clippers bench. Clippers guard Paul George had 17 points and eight rebounds in the loss.