Memphis won its third straight following a loss to the Los Angeles Clippers to open the season.
The Grizzlies opened a 13-point halftime lead and did not allow the Bucks any closer than nine during the final two quarters. Memphis hit 53 percent of its field goal attempts with Randolph going 7-of-12 while scoring 18 points.
Marreese Speights also had 18 points off the bench and Rudy Gay added 17.
Milwaukee suffered its first loss of the season, preventing what would have been the first 3-0 start for the Bucks in seven years.
Memphis took control with a 13-0 run that spanned the first two quarters.