Nuggets centre Nikola Jokic scored 16 of his 35 points in the fourth quarter, with Aaron Gordon adding 27 points and Jamal Murray ending game four in Minneapolis on 19 points.
Anthony Edwards led the overall scoring on Sunday with 44 points in total for Minnesota.
“Never underestimate the heart of a champion,” Nuggets coach Michael Malone said of his team.
“They were quick to write us off, but these guys, we won a championship a year ago.”
The Nuggets, who lost the opening two games of the semi-finals in Denver, were 64-49 ahead at half-time, but the Timberwolves rallied in the final quarter to pull within six points of the lead in the final minute.
“This team has been tested time and time again, and we’ve found a way to solve whatever has been thrown at us,” Malone said.
The series goes back to Denver for game five tonight.
In Sunday’s other game, the Indiana Pacers demolished the injury-hit New York Knicks 121-89 to level up their Eastern Conference play-off semi-final series after four games.