The Spurs lead 2-1. Their loss snapped a streak of 10 consecutive postseason wins over the Grizzlies.
Conley got most of his help from power forward Zach Randolph (21 points, eight rebounds) and center Marc Gasol (21 points, six rebounds and three assists).
Leading by four at halftime, the Grizzlies outscored the Spurs 31-17 in the third quarter and were up 81-63 entering the fourth. San Antonio coach Gregg Popovich pulled his starters early in the fourth quarter, and most did not return as Memphis stretched its lead to as much as 22 points.
Small forward Kawhi Leonard led the Spurs with 18 points. Power forward LaMarcus Aldridge scored 16 points and grabbed 11 rebounds.
The Grizzlies committed just five turnovers while cashing 12 San Antonio turnovers for 13 points.
The Spurs shot 47.2 percent from the floor and 41.7 percent (10-for-24) from 3-point range. Memphis shot 50.6 percent from the field while going 9-for-22 (40.9 percent) from distance.
The Grizzlies led 50-46 at halftime. Leonard had 16 points at the break and Randolph had 13.
NOTES: Memphis coach David Fizdale tweaked the lineup, starting PF Zach Randolph and SF James Ennis and moving PF JaMychal Green and SG Wayne Selden to the bench. Selden led the bench scoring with 10 points. ... Fizdale was fined $30,000 for his comments about the officiating after Game 2. One of his lines about the free-throw disparity -- "Take that for data" -- inspired T-shirts seen around FedExForum. ... The Spurs' last lead in Game 3 came with a minute left in the first half on a putback by LaMarcus Aldridge. ... Off the bench in Game 3 for San Antonio, Kyle Anderson had 15 points and Patty Mills scored 11.