Dallas pulled away with a 12-3 run in the final three minutes and 38 seconds, led by 33-point scorers Kyrie Irving and Luka Doncic.
If they win game four in Dallas on Tuesday at 01:30 BST on Wednesday, they will make it to the championship round for the first time since winning the 2011 championship.
“We require one additional. The Slovenian sensation Doncic stated, “Nothing’s done yet. “Their team is outstanding. We receive a break if we receive one more.”
The Timberwolves had fallen down by 12 points in the first half, but with 4:51 left in the game, Anthony Edwards made a basket.
Before Doncic and Irving increased their lead and Daniel Gafford made huge contributions at both ends of the court, PJ Washington defeated Dallas 107-104.