MEMPHIS, Tennessee (AP) -- Gregg Popovich feels like his San Antonio Spurs survived the Memphis Grizzlies and is grateful their first-round series finally is over after six games.

His Spurs desperately need a couple days off before hosting Houston on Monday night in their Western Conference semifinal.

The Spurs finished the game on a 22-8 run Thursday night after trailing by seven in beating Memphis 103-96 to take the series 4-2. Kawhi Leonard scored 29 points, and Tony Parker added 27.

"I'm seriously thrilled that we were able to get through that first round," Popovich said. "That's the good news. The bad news is that we now have to go play Houston."

The Spurs advanced by winning on the road, something neither San Antonio nor Memphis had managed against each other all season long. LaMarcus Aldridge had 17 points and 12 rebounds as San Antonio outrebounded Memphis 46-28. They got 16 of those on the offensive boards, leading to 17 second-chance points.

Parker said the Spurs treated this like a Game 7 to make sure they avoided heading home to play a deciding seventh game that had been scheduled for Saturday. That would've meant only one day to rest and prepare for the No. 3-seeded Rockets with this semifinal starting Monday night in San Antonio.

"We wanted those days off before playing Houston because it's going to be a fast-paced game against them," Parker said. "They have a great offense, and the key is going to be defense. So we're going to have to have our legs. I think this win is huge obviously, because we won the series, but even to prepare against Houston."

For much of this series, Leonard carried the Spurs as he matched or topped his playoff career high in scoring in three of the five games. He also hit his first 42 free throws of this series, the most to start a postseason series in NBA history.

But some of the other Spurs started stepping up as San Antonio turned a 2-2 tie into a series victory. Patty Mills came through in San Antonio's Game 5 win with 20 points off the bench, and he added another 10 Thursday night. Manu Ginobili ended an 0-of-15 shooting skid with 10 points off the bench in Game 5.

Parker had his best game of the series Thursday night, hitting his first six shots and finishing with 27 points. He also had two rebounds and four assists. The veteran guard, who turns 35 on May 17, was seen icing both feet and his left knee after the game but walked just fine talking to reporters.

He said he talked with Popovich about how the Grizzlies were going under on pick-and-rolls and not giving shots for Aldridge.

"I had to be aggressive," Parker said. "That's a choice that Memphis made. We talked about it last week. They just are going to leave me in the corner 3s and just go under the pick-and-rolls, so I had to be aggressive."

The Spurs easily swept the Grizzlies a year ago when Memphis had a patchwork roster with Mike Conley and Marc Gasol injured on the bench. Then they lost to Oklahoma City in six games. They agreed this series against Memphis will be much better preparation for what lies ahead.

"It's an experience that helps you push through the tough times on the floor, and that's how you gain confidence," Leonard said.

Leonard said the break also will be good for the older Spurs, plus himself after a very physical series.

"We can just regroup, get our energy back and get our bodies prepared for the next round," Leonard said. "It's going to be tougher."