Luka Doncic and Kyrie Irving each hit 36 points to lead the Mavericks to a resounding 124-103 victory in game five in Minnesota.
Slovenian star Doncic, 25, set the tone with 20 points in the first quarter before Dallas moved into a dominant 69-40 lead at half-time and the Timberwolves could not fight back.
It is the first time the Mavericks have reached the Finals since winning their sole NBA title in 2011 and only the third time overall.
They beat the Los Angeles Clippers in round one before reaching the conference finals with victory over top seed the Oklahoma City Thunder.
The best-of-seven NBA Finals begin in Boston on Thursday.
The Celtics are chasing a record 18th NBA title in their 23rd Finals appearance.
Anthony Edwards and Karl-Anthony Towns each scored 28 points for the Timberwolves, who beat the Phoenix Suns 4-0 in round one before stunning defending champions the Denver Nuggets in the conference semi-finals.
But their usually superb defence could not stifle the sublime Doncic throughout the series.
“It was Luka magic mode,” said Mavericks head coach Jason Kidd.
“He set the tone and then he made it easier for everyone else. Everybody else stepped up.”
Irving took over the scoring in the second quarter and will now appear in his first NBA Finals since 2017.
“I was enjoying it, you’re just watching a special performance take place,” said Irving.
“When Luka starts off a game like that, we’re a tough team to beat.”