"This builds our confidence up a lot," Randolph said. "We've got young guys, and when we win games like this, this is believing in us [as a] team that we can beat anybody."
Randolph's rebound total, which included nine on the offensive end, was the highest in the league this season. His work down the stretch allowed Memphis to weather a Denver rally that got the Nuggets within two points with 3 minutes, 22 seconds left when Carmelo Anthony (41 points) hit an 18-foot jumper.
Randolph's three-pointer with 43 seconds left, only his third trey of the season, gave Memphis a 100-91 lead.
"I think Zach is in a great comfort place," Grizzlies coach Lionel Hollins said.
In other games:
* At Boston, Paul Pierce scored 29 points to lead the Celtics to a 122-104 victory over Minnesota. Kendrick Perkins had 14 points to go with 11 rebounds, and Rajon Rondo had 13 points and 15 assists as the Celtics beat the Timberwolves for the sixth consecutive time since acquiring Kevin Garnett in a seven-for-one deal during the summer of 2007.
* At Toronto, Chris Bosh had 25 points and 11 rebounds and the Raptors beat New Orleans, 98-92. David West had 21 points and 12 rebounds for the Hornets, who lost for the 11th time in 13 road games.
* At New York, Wilson Chandler scored 26 points, Danilo Gallinari added 21 and a huge blocked shot in the closing seconds, and the Knicks held on for a 98-94 victory over the Charlotte Bobcats, whose Raymond Felton had 27 points, nine rebounds and seven assists.
* At Dallas, Tim Thomas took Dirk Nowitzki's spot in the starting lineup and did a nice impression with 22 points, helping the Mavericks beat the Cleveland Cavaliers, 102-95. Nowitzki was recovering from a collision with Houston's Carl Landry on Friday in which Landry lost five teeth, two of them becoming embedded in Nowitzki's right elbow. He needed several stitches to close the wound and was still too sore yesterday.
* At Auburn Hills, Mich., Kobe Bryant scored 28 points as the Los Angeles Lakers rolled to a 93-81 victory over Detroit.
* At Miami, Brandon Roy scored 11 of his 28 points in the fourth quarter, LaMarcus Aldridge added 22 and the Portland Trail Blazers used a big run in the final minutes to beat the Heat, 102-95. Dwyane Wade had 28 points and 10 assists for Miami.
* Dallas owner Mark Cuban officially filed a protest with the NBA office yesterday over what he termed "misapplication of the rules" by the officiating crew during Friday's overtime loss to Houston. Cuban said the officials were wrong to eject Mavericks center Erick Dampier in the OT, for throwing an elbow.