HOUSTON -- After seeing what the Memphis Grizzlies had done in their previous two games, the Houston Rockets knew how important hitting their shots late in the fourth quarter would be on Monday night.

Kyle Lowry scored 24 points, Kevin Martin added 22 and Courtney Lee made four key free throws down the stretch as the Rockets held off the Grizzlies 97-93.

The Grizzlies had won their last two games by one point on tip-ins in the last few seconds, but their late-game magic ran out Monday as their four-game winning streak was snapped.

"Anytime in the fourth quarter in close games like that where you can get a little bit of separation, those plays are huge," Lee said.

Houston led by seven before Memphis went on a 5-0 run to get within 91-89 with 27.4 seconds left. O.J. Mayo grabbed a rebound, took it down the court and finished with a layup to cap that spurt.

Lee made a pair of free throws before Rudy Gay's layup with 19 seconds remaining got Memphis back within two points.

Lee hit two more free throws and Quincy Pondexter's layup cut it to two again before two free throws by Lowry secured the win.

"We played it right to the end," Memphis coach Lionel Hollins said. "We got close, but we couldn't make them flinch or blink at the free throw line."

Gay led the Grizzlies with 23 points and Mike Conley had 16.

"Kyle was the difference," Gay said. "He controlled the game. It's tough when he plays like that, when he drives and shoots like that. He played really well."

Luis Scola scored 10 points for Houston and Lee finished with nine -- all in the fourth quarter.

The loss left Memphis without a win in Houston in 11 tries, with its last victory in the city coming in 2006.

The Grizzlies didn't make a basket in the fourth quarter until Tony Allen's layup with 5:44 remaining. He followed with another one seconds later to cut Houston's lead to 86-82.

The Rockets pushed the lead to 91-84 with just under 2½ minutes remaining before Memphis went on the run that cut the lead to two with less than 30 seconds remaining.

Houston opened the fourth quarter by scoring 10 straight points, capped by a 3-pointer from Lee, to break a tie and take an 86-76 lead with about 9 minutes to go.

The Rockets thought they weren't physical enough in two losses to Memphis earlier this season and wanted to change that Monday night.

"We had to go out there and play a little bit tougher than they did," Lowry said. "I think that ... they definitely out-toughed us (before) and tonight we made it a point to out-tough them."

The Rockets led by seven early in the third before the Grizzlies used a 9-2 run to tie it at 63 with 7 minutes left in the quarter. Conley had five points during that spurt.

Memphis took a five-point lead a few minutes later, before Houston outscored the Grizzlies 7-2 at the end of the third quarter to tie it at 76 entering the fourth. Lowry, who finished with nine assists, scored all of Houston's points in that run.

The Grizzlies held Martin scoreless for the first time in six years in a 93-83 win last Tuesday in Memphis.

He outdid his performance in that game when he made his first shot -- a 3-pointer with just more than 10 minutes left in the first quarter, and had 18 by halftime.

Houston's Goran Dragic got hit in the nose in a collision with Dante Cunningham while vying for a loose ball late in the third quarter. Dragic, called for a foul on the play, remained on the court for a bit while trainers checked him out. He left the game but returned just a few seconds later.

Houston coach Kevin McHale said Dragic was already feeling bad before being hit in the face because of a stomach ailment and the coach said he was happy Dragic was able to play Monday. Dragic didn't look great after the game, and said he vomited at halftime.

The Rockets led 58-54 at halftime after shooting a season-high 66.7 percent in the first half.

Game notes
Houston recalled F Marcus Morris from Rio Grande Valley of the D-League. ... Rockets C Hasheem Thabeet missed the game with a sore lower back. ... The Grizzlies controlled the paint, outscoring Houston 58-38 in that area. ... Houston's Patrick Patterson had a season-high nine rebounds.