Jonas Valanciunas and Amir Johnson scored 15 points apiece for Toronto, and Jose Calderon had 11, while matching Lowry's seven assists. Bargnani was 6 of 12 from the field, including 3 for 4 from 3-point range.
Jerryd Bayless led Memphis with 17 points. Quincy Pondexter finished with 16 and Tony Allen 15.
The Grizzlies rested starters Rudy Gay, Mike Conley, Zach Randolph and Marc Gasol.
Memphis led 66-59 at halftime behind 13 points from Bayless, while Bargnani scored 13 for the Raptors.
Toronto didn't take its first lead until midway through the third. The Raptors outscored Memphis 32-21 in the period.