Bulls rookie Derrick Rose, last spring's No. 1 draft pick, played nearly 27 minutes and scored 10 points in Chicago's preseason opener.
Dallas (2-0) never trailed, using an 11-1 run in the first quarter to establish an early edge. Josh Howard scored six points during that span and finished with 10.
The Mavs' lead ballooned to 19 points by halftime, then slipped to seven after the Bulls opened the second half with a 12-0 run. Rose had a pair of long-distance jumpers during the surge, which ended with Dallas guard Gerald Green's 20-foot field goal at the 6:59 mark.
Chicago trailed 82-70 after three quarters but rallied to within six points with 1:56 left.
Luol Deng, Aaron Gray and Darius Washington paced the Bulls with 14 points each, while Drew Gooden and Larry Hughes each added 11.
Dirk Nowitzki scored 15 points for the Mavericks, Antoine Wright and Jose Barea each had 11 and Brandon Bass added 10.
Rose had a slow start in his NBA debut. The former Memphis guard missed his first four field goal attempts before scoring on a right-handed layup with 6:45 left in the second quarter.
Four Chicago players -- including regulars Joakim Noah and Ben Gordon -- sat out with injuries.