Randolph added 12 rebounds, Tony Allen scored 16 points, connecting on 8 of 12 shots, and Mike Conley finished with 15 points and 10 assists. Reserve Jerryd Bayless added 14 points and Tayshaun Prince finished with 10.
Allen also had a strong defensive effort in limiting Rockets' star James Harden, who came into the game fifth in the league in scoring with a 26.2 average, to seven points on 3-of-9 shooting.
Chandler Parsons and Donatas Motiejunas led the Rockets with 16 points apiece, despite not playing in the fourth quarter as Houston coach Kevin McHale used his reserves to try to put more pressure on the Grizzlies defensively. Carlos Delfino had 15 points for Houston, while James Anderson had 10.
The victory came after Memphis had lost two straight on the road, at Washington and New York. The Grizzlies now have won 11 straight at home.
Houston dropped its second straight game.
Gasol and Randolph led an inside dominance for Memphis as the Grizzlies held a 56-46 advantage in the paint and outrebounded the Rockets 42-35.
Memphis opened the second half with a 19-10 rally to stretch its 61-53 halftime lead to 80-63, its biggest of the game. Memphis turned up the defence from the start of the half after Allen got a steal on the Rockets' opening possession and broke free for a dunk, and the first double-digit lead of the game.
Gasol had eight points in the quarter as Memphis outscored Houston 23-16 in taking an 84-69 advantage into the fourth quarter.
In the fourth, it was the Rockets' reserves who were applying the defensive pressure, leading to an 8-2 rally, fueled by four Memphis turnovers. That cut Houston's deficit to single-digits. Anderson and Delfino both had four points in the push.
Memphis immediately answered, extending the lead as Randolph began working inside, scoring six straight points as the Grizzlies regained the momentum.
Memphis maintained the double-digit advantage until Anderson's jumper in the closing seconds provided the final score.
Both teams shot well early. Memphis was at 60 per cent after the first quarter, while the Rockets were at 55 per cent, including connecting on 5 of 8 outside the arc.
Those trends continued through the half as Memphis shot 62 per cent to take a 61-53 lead into intermission.
The Rockets dropped a bit on field goal percentage, but still connected on 7 of 16 from long range.
Randolph, who has struggled offensively recently, already had 15 points, matched by 15 from Parsons.
Memphis would end the night shooting 51 per cent, while Houston connected on 42 per cent.
NOTES: Friday's game at Memphis was the Rockets' only road trip in a 10-game stretch. Houston finished 5-2 in its previous seven games, all at home. The Rockets play their next two back at the Toyota Center against the Clippers and the Magic. . The Rockets have lost five straight in Memphis. . Memphis entered the game having given up an average of 107 points in its last three games.