Sam Young scored 18 points and the Grizzlies dominated the league's best rebounding team on the boards, 47-38, to win their fourth straight game.
Michael Beasley scored 19 points for the Timberwolves and Kevin Love had just 10 points and 10 rebounds, narrowly getting his 34th straight double-double. Love is hoping to make the Western Conference All-Star team, but he was thoroughly outplayed by Randolph, one of his primary competitors for a spot.
The Grizzlies limited Love to four points on 1-for-4 shooting in the first three quarters, opening up a 22-point lead that turned the fourth quarter into garbage time.
The Grizzlies are the best team in the league at forcing turnovers, and they feasted on the mistake-prone Timberwolves all night. They scored 26 points off 17 Minnesota turnovers and improved to a season-best two games over .500 (26-24).
Beating the worst team in the West wouldn't seem to be a big deal, but it actually was a sign of progress for the young and improving Grizzlies. They have had a tendency to play down to their competition this season, losing to Golden State, Washington, Cleveland, Sacramento and New Jersey twice.
But this game was never in doubt.
Memphis ripped off a 10-0 run midway through the first quarter and never trailed the rest of the way.
Gay showed everyone why the Timberwolves tried to sign the restricted free agent this summer. The smooth small forward, who signed a max contract to stay in Memphis, did a little bit of everything, getting to the bucket, knocking down 3-pointers and scoring in transition.
Randolph and Marc Gasol took care of Love down low, muscling him out off the block and rendering him obsolete for most of the game.
The game featured a matchup of two of the NBA's double-double machines in Love and Randolph. They are two of just four players in the NBA to average at least 20 points and 10 rebounds per game, but it was Randolph who had his way with it from the start.
The burly Randolph had eight points and six boards in the first half, and more importantly limited Love to just two points and four boards on the other end.
The Timberwolves were listless all game, delivering an uninspired performance despite coming off a win over Toronto on Saturday, a day off on Sunday and two practices to prepare for this game.
Darko Milicic had three points on 1-for-6 shooting with two rebounds and five turnovers in 20 minutes and Wes Johnson had just four points on 2-for-11 shooting.
Notes: Memphis coach Lionel Hollins' son Austin is a freshman at the University of Minnesota. But dad said he doesn't watch his son play very often "because I don't like college basketball." Lionel said he gets frustrated by the slow pace. ... Minneapolis Mayor R.T. Rybak sat in for a portion of the television broadcast to tout the plan for renovating Target Center. The city and the Wolves are asking for $155 million to update the 21-year-old facility. ... The Wolves played without PG Luke Ridnour, who missed the game to tend to a family matter.