Butler's 22-footer with 5:22 left gave Dallas (1-1) the lead for good at 76-75. He scored his team's next seven, capped by a 3-pointer with 3:14 to play that extended the Mavericks' advantage to 83-75.
Derrick Rose scored 17 points for Chicago (0-2). Center Joakim Noah, who agreed to a five-year, $60 million contract extension on Sunday, had 13 points, eight rebounds and six assists.
Nowitzki's 3-pointer with 2.3 seconds left in the second quarter gave Dallas a 45-44 edge at the break. The Mavericks carried a 66-63 lead into the final quarter.