Jason Terry added 10 of his 17 points in the final quarter for the Mavericks (1-3), who hadn't started 0-4 since the 2006-07 season.
The last defending NBA champs to open a season at 0-4 were the 1969-70 Boston Celtics.
Andrea Bargnani scored 30 points and Leandro Barbosa had 20 for the Raptors, 1-2 under first-year coach Dwane Casey, Dallas' top assistant and defensive architect last season.
Toronto used a 17-2 run in the third quarter, completed by Amir Johnson's follow dunk, for a 68-61 lead.
But Dallas finished the quarter with a 16-2 spurt, capped by Vince Carter's three free throws, for a 77-70 edge heading into the fourth quarter.
Toronto never got closer than five points the rest of the way.
The Mavericks carried a 29-23 lead into the second quarter, riding a 17-6 rebounding advantage in the opening 12 minutes.
Dallas got off to a better defensive start, a point of emphasis by coach Rick Carlisle. The Mavs had allowed 32, 32 and 28 points in the first quarter of their three games.
The Mavericks went on to lead by as many as 12 in the second quarter.
But Bargnani scored 13 of his 18 first-half points in the period, and Toronto's late 12-0 run narrowed the halftime gap to 50-46.
NOTES: Mahinmi's previous career high was 17 points at Memphis on Jan. 15, 2011. ... The teams met for the only time this season. ...Dallas has won 11 of 12 at home against Toronto. ...Nowitzki had converted 22 straight free throws before a miss in the opening quarter. ... G Jerryd Bayless twisted his left ankle with 9:14 left in the second quarter. Bayless attempted to run, but was playing on one leg and limped to the locker-room six seconds later, done for the night. ... Players from Penn State and Houston were in the crowd. The teams meet Jan. 2 in the TicketCity Bowl in Dallas.