Mike Conley finished with 14 points and seven assists for Memphis, and Ed Davis scored 10.
Aaron Afflalo had 20 points, six rebounds and seven assists for Orlando. Mo Harkless scored 19, and Andrew Nicholson added 14 points. E'Twaun Moore scored 12 points and handed out seven assists as the Magic dropped their fourth straight and 16th in their last 17.
The Magic had only seven players available because of injuries and trades from Thursday that sent players to Milwaukee. The returning players were not available.
Memphis outrebounded the Magic 52-42, including 14 offensive boards. Memphis' biggest shortfall was at the free-throw line, where the Grizzlies were 17 of 29. The Magic only went to the line nine times in the game, converting seven of them.
There were 15 lead changes and five ties but those came in the first half.
The Magic dropped off the pace when they were outscored 24-15 in the third. The lead reached as many as 13 in the quarter as Memphis' defense disrupted the Orlando offense.
Quincy Pondexter's 3-pointer in the closing seconds of the third extended the lead to 67-53. Randolph had eight in the quarter for Memphis.
The Grizzlies' opening basket of the fourth ran the lead to 16, but Orlando answered with eight straight points.
But Orlando's rally fizzled when Nikola Vucevic fouled out with about 8 minutes to play, and Nicholson fouled out less than 4 minutes later. Then all the players available for the Magic had to play out the rest of the game.
Tayshaun Prince, Randolph and Gasol scored consecutive baskets to finally give Memphis enough of a buffer to extend the Grizzlies' winning streak.
Orlando stayed close in the first half, but the Grizzlies scored the final eight points of the second to carry a 43-38 lead into the break.
Gasol had 11 points at intermission, while Harkless and Afflalo each scored nine points for Orlando.
NOTES: The Magic were without J.J. Redick, Gustavo and Ish Smith, who were traded at Thursday's deadline, and players they got in return - Tobias Harris, Doron Lamb and Beno Udrih - were not with the team yet. ... The Grizzlies have now held 46 of 54 opponents under 100 points. ... Randolph recorded his 33rd double-double, Gasol his 11th.