Houston has lost three straight to drop to 1-3 since coach Kevin McHale was fired and replaced by J.B. Bickerstaff.
The Grizzlies led for most of the game despite playing without Zach Randolph, who missed his fourth straight game with soreness in his right knee.
Lee made the first points of the fourth quarter for Memphis with about 9 minutes left. It was the first of six straight points for Lee, a former Rocket, that pushed the lead to 88-79.
James Harden had 40 points for the Rockets. They are 5-10 overall.
The Rockets made eight free throws in the first almost 10 minutes of the fourth quarter, but did not make a field goal until a 3-pointer by Jason Terry cut it to 98-88 with 2:01 remaining. Houston missed eight shots and had four turnovers in the fourth before Terry's shot.
Corey Brewer made a 3-pointer after that, but Lee struck again, making a jump shot seconds later to make it 100-91 with just over a minute left.
The Grizzlies led by five after three and neither team scored in the fourth until Trevor Ariza made a pair of free throws with 9:32 left in the quarter. About the only excitement in the beginning of that quarter came when Dwight Howard and JaMychal Green got tangled up fighting for a rebound and pushed each other, drawing a technical foul for both players.
The Rockets were down by eight in the third quarter before they used a 9-3 run, with six points from Harden, to get within 66-64 with 8 1/2 minutes left in the quarter. But an 8-2 spurt by Memphis after that pushed the lead to 74-66 just a 1 1/2 minutes later. Tony Allen led the way during that stretch with four points and the Rockets had three turnovers.
Harden hit a 3-pointer soon after that, but Houston's offense went cold after that and the Rockets didn't make another field goal until a layup by Pat Beverley with 2:18 left in the quarter.
Those were the first of five straight points for the Rockets that get them to 80-77 with just over a minute left in the quarter.
Jeff Green made a pair of free throws to extend the lead to 82-77 entering the fourth quarter.
Harden had a chance to them closer as time expired in the third, but Green blocked his layup into the crowd.
The Grizzlies led by as many as 12 in the first half, but Houston cut it to 56-53 at halftime.
Grizzlies: Improved to 9-0 when leading at the half. ... Mike Conley added 19 points for Memphis. ... Marc Gasol had 11 points and 16 rebounds.
Rockets: Beverley returned after missing five games with a sprained left ankle. He had four points and two assists. ... Howard finished with 12 points, five rebounds and three steals.
Grizzlies: Host the Hawks on Friday night.
Rockets: Host the 76ers on Friday night.