The Grizzlies hit 72.2 percent of their shots in the third quarter while outscoring Toronto 33-14. That outburst came after Memphis had owned only a one-point halftime lead.
Memphis, which has an NBA-low two losses this year, won its third straight.
Marreese Speights had 18 points and 12 rebounds off the bench to pace Memphis while Zach Randolph joined Gasol with 17 points. Mike Conley, after missing a game with flu-like symptoms, added 16.
Toronto lost its sixth straight game. DeMar DeRozan scored 16 points for the Raptors while both Kyle Lowry and Jose Calderon had 12. Toronto played without Andrea Bargnani, who sat out with a sore left ankle.