Edwards made 17-of-29 shots from the floor, 3-of-7 from 3-point range, and all six free throws for his third career 40-point playoff game.
"My teammates trust me in every position in critical moments in the game. I try to come through for them," Edwards said after Minnesota took a 1-0 lead in the best-of-seven Western Conference second round series, which continues on Monday in Denver.
"It's tough here," Edwards said. "The altitude, their team, the crowd. I'm proud of my teammates. They came out and fought super-hard."
None delivered more in the clutch than NBA Sixth Man of the Year Naz Reid, who scored the first 10 Minnesota points in an 18-7 run to break an 84-84 deadlock. Reid scored 14 of his 16 points in the last quarter.
Anthony and his teammates kept the Nuggets at bay to the finish, with "Ant-Man" crediting his time with the 2023 US Basketball World Cup team with improving him this season.
"I put in work this summer," said Edwards. "Shout out to USA team. They got me ready for this season. I appreciate that."
Karl-Anthony Towns, whose foul trouble late led to Reid entering the game, scored 20 points while Mike Conley added 14 points, all in the second half, plus 10 assists and Rudy Gobert grabbed 13 rebounds.
The Nuggets, who hadn't trailed in a playoff series in two years, were led by 32 points, nine assists and eight rebounds from two-time NBA Most Valuable Player Nikola Jokic.
But the Serbian center was pressured into a game-high seven turnovers and rushed into shots by an aggressive T-Wolves defensive effort.
Michael Porter Jr. added 20 points for Denver while Jamal Murray had 17, all in the second half after his first scoreless playoff half in 59 post-season contests.
Edwards scored 25 of Minnesota's 40 first-half points on 10-of-17 shooting, keeping the T-Wolves within 44-40 at halftime.
Edwards netted 16 first-quarter points, 11 of them in a 14-2 Minnesota run to start the contest. But the Nuggets answered with a 21-3 spurt that put them ahead 25-23 after the first quarter, in which Jokic and Porter each scored nine points.
Timberwolves coach Chris Finch, who underwent surgery Wednesday to repair a ruptured patellar tendon in his right knee, was seated a row behind the players in order to guide his club.
