Memphis won its fifth straight, holding the Nuggets to 11 points in the first quarter and never getting threatened the rest of the way as Randolph recorded his 10th consecutive double-double.
Wilson Chandler and Kenneth Faried each scored 10 points for Denver, which lost for the eighth time in the last nine.
With Memphis comfortably ahead at the end of the third quarter, both teams relied on their reserves to finish out the fourth.
Memphis outrebounded Denver, 57-47, and held a 46-42 advantage in the paint. The Nuggets managed to shoot only 33% for the night and were two for 26 from outside the arc — less than 8%. Memphis was only slightly better at three for 16.
Struggling Indiana (17-31) picked up its most lopsided home victory of the season by winning for only the second time in 10 games.
Carmelo Anthony scored 18 points, 12 in the first 9 minutes for the Knicks (9-38). Lou Amundson added 17 as New York managed just 33 second-half points and fell behind Philadelphia for the worst record in the East.
The Bucks never trailed and placed seven players in double figures, including all five starters. Brandon Knight had 16 points and eight assists, O.J. Mayo scored 13 points and John Henson had 12 points and 11 rebounds.
The Magic has lost seven straight and 13 of its last 15 games. Victor Oladipo led Orlando with 21 points. Nik Vucevic added 17 points and 14 rebounds.