The Jazz responded by converting five straight possessions. Paul Millsap and Jamaal Tinsley scored four points during an 11-2 run that gave Utah a 15-10 lead with 6:08 remaining.
The Timberwolves started going inside, however, and regained a 24-23 lead by the end of the quarter.
Led by Earl Watson, Enes Kanter and Hayward, Utah built a 38-28 lead with just under eight minutes left in the half.
Kanter scored eight points before picking up his third foul, while Hayward added seven during the Jazz's best stretch of the game.
They took a 53-45 lead at halftime.
In the third quarter, Minnesota failed to convert its opening eight possessions.
The Jazz scored 11 straight points and eventually took a 70-50 lead after Paul Millsap scored eight points in six minutes.
The Timberwolves stayed close, though, by making 10 straight free throws in the final 5:43. They trailed 79-66 heading into the final 12 minutes but never got closer.
Before the tipoff, the Jazz learned they will be without starting point guard Mo Williams for at least six weeks because of thumb surgery.
Williams averages 12.9 points and 6.7 assists. His thumb will be placed in a splint for six weeks. He will be limited to conditioning and restricted weight lifting before being re-evaluated in six weeks.