SAN ANTONIO -- Kawhi Leonard poured in a career-playoff-high 37 points, and five San Antonio players scored in double figures as the Spurs defeated the Memphis Grizzlies 96-82 on Monday at the AT&T Center in Game 2 of a Western Conference first-round playoff series.

San Antonio, the West's second seed, leads the best-of-seven series 2-0 as the action moves to Memphis for Game 3 on Thursday and Game 4 on Saturday.

The Spurs built a 26-point lead in the first half and had to fight off a comeback from never-say-die Memphis, which cut San Antonio's advantage to four points early in the fourth quarter but could never get over the hump.

Tony Parker added 15 points for San Antonio. Danny Green scored 12, LaMarcus Aldridge pumped in 11 points and Pau Gasol contributed 10 points off the bench. Leonard also took 11 rebounds and converted all 19 of his free-throw attempts.

Mike Conley led the Grizzlies, the seventh seed in the Western Conference, with 24 points. Zach Randolph added 18 points and 10 rebounds off the bench, and Marc Gasol and Vince Carter hit for 12 points each for Memphis.

The Spurs took charge in the opening quarter, leading by as many as 13 points, including at the end of the period, when a put-back layup by Pau Gasol gave San Antonio a 29-16 advantage. Every Spurs starter scored in the first 12 minutes and San Antonio went 12 of 12 from the free-throw line. Memphis hit just 6 of 25 shots in the quarter (24 percent) and took only three free throws.

San Antonio kept pouring it on in the second quarter and the Grizzlies had no answer, growing more frustrated with every empty possession.

Memphis' Vince Carter got a technical foul going face to face to heatedly debate with Spurs' reserve guard Kyle Anderson. Late in the period Conley, trapped by stifling defense by San Antonio's Manu Ginobili along the sideline in front of the Grizzlies' bench, called time out, flipped the ball behind his back into the court and strode right off the floor and into a chair.

San Antonio owned a 56-37 lead at the half with Leonard pacing all scorers with 18 points. The Spurs went to the charity stripe 23 times in the first two quarters, making 22 of them, while Memphis was just 5 of 6 on free throws, a 17-point difference in a 19-point game.

Conley led Memphis with 14 points, one more than he had total in the first game of the series. Marc Gasol, who had 25 points in the first half in the series opener on Saturday, scored only three points in the first half Monday on 1-of-8 shooting.

The Grizzlies are nothing if not gritty and they battled to within 11 points at the 6:08 mark of the third quarter by outscoring San Antonio 13-5 in the first six minutes of the period. Memphis' increased physicality and aggressiveness was enough to allow it to head to the fourth quarter down just 75-65, well within striking distance.

Memphis scored the first six points of the fourth quarter to crawl to within 75-71 but the Spurs responded with a Leonard jumper and a Parker 3-pointer to create a little breathing room.

NOTES: Spurs F/C Pau Gasol played 476 games for the Grizzlies from 2001-08, winning the 2001-02 NBA Rookie of the Year Award and becoming the franchise's first-ever All-Star (2006). Gasol is also fourth in franchise history for points scored (8,966), holding the franchise record until he was passed by Mike Conley (and later Marc Gasol and Zach Randolph) earlier this season. ... Grizzlies F JaMychal Green split his rookie season (2014-15) with San Antonio and Memphis. He averaged 2.0 points and 1.5 rebounds in four games with San Antonio following a successful stint with the NBA Development League's Austin Spurs. ... This series marks the seventh time Memphis has met a postseason opponent that won at least 60 games during the regular season. The Grizzlies have won two of the previous four postseason series against 60-plus win opponents.