Rudy Gay had 23 points for Memphis, which used defensive pressure in the final period to outscore Denver 34-18. Tony Allen, who added 17 points, energized the defense while Randolph scored 12 of his 14 points in the fourth.
Mike Conley also had 17 points for Memphis and Marc Gasol added 15 - all in the first half.
Carmelo Anthony, who entered averaging 32.8 points per game in February, finished with 28 - his sixth game in the last seven with at least 25 points.
Nene, Ty Lawson and J.R. Smith scored 14 points each for Denver. Chauncey Billups had 13 points and seven assists.
Denver had won 11 of the last 12 in the series, but the Grizzlies took this one by outscoring the Nuggets 20-6 in the final 7:09.
Memphis shot well early, but the Nuggets opened the second quarter by hitting their first seven shots to build a 16-3 run. They connected on 12 of their first 13 attempts in the period.
Denver scored consistently at the rim. Nene got his share of dunks, as well as Chris Andersen and Anthony, including Anthony's jam with 1:31 left in the half to give the Nuggets their first double-digit lead.
Denver outscored Memphis 41-24 in the second quarter, helping the Nuggets to a 67-55 lead at the break. They shot 18 of 25 in the period.
Anthony had 15 points for Denver, while Nene and Smith scored 10 each.
Gay had 13 points in the half.
The Nuggets maintained the pace through most of the third quarter, extending the lead to as many as 17. Memphis, which had six turnovers in the period, made a bit of a run in the final minutes to get the deficit to 86-77.
Anthony scored 11 in the period and Denver had a 90-82 lead after three.
Memphis amped up its defensive pressure to start the final period and chiseled away at the advantage. The Grizzlies tied it at 96 on two free throws by Conley with 8 minutes left. Just more than 2 minutes later a pair of free throws by Arthur gave Memphis a 102-100 lead, and the Grizzlies never trailed again.
NOTES: Grizzlies G O.J. Mayo finished serving his 10-game suspension for violating the NBA's drug policy. Mayo will return Tuesday against Philadelphia. ... Nuggets coach George Karl said he is pleased with the way his players have handled the Anthony trade rumors, giving them anywhere from an A to a B+. "Mental toughness is a part of being a professional athlete," Karl said. "Has it filtered into our locker room at times because it is with us after a bad loss or a tough loss? Yeah. But in general, I think we've kept our focus." ... Randolph returned to action after missing Friday's win over Milwaukee with a balky right ankle.