Jamal Crawford added 20 points and seven assists off the bench for the Timberwolves, who rallied from 14 down to end Denver's eight-game home winning streak.
The Nuggets were without leading scorer Gary Harris and backup point guard Emmanuel Mudiay, forcing coach Michael Malone to use his 13th different starting lineup. Malone went with a bigger group and started Nikola Jokic and Mason Plumlee together for the first time this season.
It worked for most of the game, but the Nuggets faltered after taking an 80-66 lead late in the third quarter.
Jamal Murray led Denver with 30 points. Plumlee added 17 points and 10 rebounds, and Jokic had 22 points, six rebounds and 10 turnovers.
Butler started slowly two nights after scoring 37 points and hitting 11 of 12 free throws against Portland. He scored 11 points in the fourth, including nine in a row to carry Minnesota to the win.
Towns scored the first 11 points for Minnesota. The Timberwolves used a 19-4 run in the third and fourth to go up by one.
Crawford sparked an 11-2 spurt midway through the fourth to give the Timberwolves a 102-95 lead.
Timberwolves: Jeff Teague had 16 points and eight assists. ... Minnesota had nine turnovers, one fewer than Jokic had on his own. ... F Nemanja Bjelica, out since Nov. 22 with a sprained left midfoot, was going through drills before the game and shooting 3-pointers from long range. He is close to returning but missed his 14th straight game.
Nuggets: Harris was injured on a hard fall at Oklahoma City on Monday. He is averaging 16.1 points per game. ... Mudiay missed his second straight game with a sprained right ankle. He is day to day. ... G Monte Morris was recalled from Rio Grande of the G-League. With Tyler Lydon and Torrey Craig also up, all of Denver's G-League players are with the team. ... Denver Broncos LB Von Miller sat courtside. He autographed a football and threw it into the stands in the third quarter.
Timberwolves: Play at Phoenix on Saturday night.
Nuggets: Travel to Portland to face the Trail Blazers on Friday night.