Western Conference top seeds Denver, led by 43 points from reigning two-time Most Valuable Player Nikola Jokic, closed regulation on a 12-0 run to force overtime.
But they were out-scored 18-12 in the extra session at the Target Center in Minneapolis as the Timberwolves pulled within 3-1 in the series.
Minnesota still face a daunting task -- no NBA team has come back from 3-0 down to win a best-of-seven series.
"See you in Denver, we're going back," said Edwards, whose 16 third-quarter points keyed a Timberwolves charge that carried them to a 12-point lead midway through the fourth.
Mike Conley added 19 points for Minnesota. Karl-Anthony Towns scored 17 points with 11 rebounds and Rudy Gobert added 14 points and 15 rebounds as the Timberwolves withstood another big night from Jokic.
The Serbian star matched his playoff scoring high and added 11 rebounds and six assists.
The teams swapped the lead four times in overtime, but Nuggets coach Michael Malone said too many defensive lapses in the extra session doomed his team.
"You hold them to 16 points in the fourth quarter, then (they have) 18 in five minutes," Malone said. "That's the hardest thing to stomach about this game is that when the game was on the line, we were unwilling and unable to get the necessary stops."
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'SLOPPY' CURRY
It was the second Western Conference thriller of the day, after the Golden State Warriors held off a ferocious fourth-quarter fightback from the Sacramento Kings to secure a 126-125 victory that levelled their series at two games apiece.
Harrison Barnes almost snatched victory for Sacramento at the buzzer, but his long-range effort bounced off the rim to leave the NBA champions celebrating.
Stephen Curry led the Warriors with 32 points -- and breathed a sigh of relief after two uncharacteristic blunders in a frenetic finale at the Chase Center.
Curry missed a wide-open three-pointer with his team leading 126-121 with less than a minute remaining.
He then erroneously called a timeout when the Warriors had none left, earning a technical foul and allowing Sacramento's Malik Monk to make it a four-point game with a free throw.
De'Aaron Fox's three-pointer pulled Sacramento within 126-125 and Curry missed another floater to give the Kings a final chance.
"It was kind of sloppy not knowing how many timeouts we had left, and a couple of dagger shots didn't go in -- but we did what we needed to do defensively in those last 10 seconds," a relieved Curry said.
Klay Thompson added 26 points and Jordan Poole had 22. Draymond Green, back from suspension, scored 12 points with 10 rebounds and seven assists off the bench to help the Warriors withstand a 38-point performance from Fox.
KNICKS AND CELTICS CLOSE IN
In the Eastern Conference, the New York Knicks and Boston Celtics moved within a victory of advancing, the Knicks beating the Cleveland Cavaliers 102-93 and the Celtics downing Atlanta 129-121 to each take 3-1 series leads.
Jalen Brunson drained five three-pointers on the way to 29 points for the Knicks, who again electrified Madison Square Garden.
With just one win from three more games the Knicks can advance past the first round for the first time since 2013.
Darius Garland led Cleveland with 23 points but Donovan Mitchell scored just 11 -- only two in the second half.
The Cavs will try to extend the series when they host game five on Wednesday.
The Celtics can wrap up their series at home on Tuesday after bouncing back from a disappointing game-three defeat with a convincing victory in Atlanta.
Jayson Tatum and Jaylen Brown scored 31 points apiece for the Celtics, each delivering a dunk in the final minute as the Celtics thwarted the Hawks' final rally bid.
Hawks star Trae Young finished with a game-high 35 points and handed out 14 assists.
But Boston stepped up their defensive intensity and had an answer for every Atlanta run, never trailing after the first quarter.
Brown got off to a slow start, making just one of his first seven shots. Then he got rid of the protective mask he's worn since suffering a facial fracture in February and made 11 of 15.
"Maybe it was all in my head," Brown said. "I took it off and started to turn things around a little bit."
