Dallas trailed by 16 at the start of the fourth quarter but outscored the Jazz 44-18 to grab the win.
"My mentality in the fourth was to go out there and make things happen," said Nowitzki, who also had 11 rebounds, five assists and five blocked shots. "I think what really helped was we got to the bonus real quick in the fourth by being aggressive and driving to the basket. We were shooting free throws the rest of the way and that helped us get back into the game."
Nowitzki made all 14 of his fourth-quarter free throws while the Jazz scored just one field goal in the final 3:49 of play.
Jason Kidd added 19 for the Mavericks, who won their third consecutive game.
Deron Williams scored 22 points for the Jazz and Mehmet Okur contributed 14 points and 14 rebounds.