Memphis point guard Mike Conley had an opportunity to win the game, but his 29-foot 3-point attempt fell short at the buzzer.
"I told the guys at the (beginning of) overtime that it was all a mental contest," Spurs coach Gregg Popovich said. "It would be easy to go down after losing the lead and playing as sloppily as we did at the end of the game. It would be easy to hang your head. So I thought that was the most important thing: letting go and moving forward mentally."
Tim Duncan led the Spurs with 24 points — including six in overtime — while Marco Belinelli added 19 and Kawhi Leonard 17. Conley had 30 points, one off his career high, for the Grizzlies, scoring 21 in the second half.
"(The Grizzlies) had some great plays down the stretch there," Duncan said. "We thought there was a couple of fouls missed (but) they played horn to horn and we didn't. We slacked off there for a minute, but luckily not enough to be able to regroup in overtime and find a way to win."
Memphis trailed by 16 with five minutes left in regulation, and used a 23-7 run to rally and force overtime. Conley hit a runner at the end of regulation to send the game into overtime 3 seconds after Ginobili had scored on a layup.
"I was proud of the effort at the end," said Grizzlies coach Dave Joerger. "We kept coming. We started to attack them the way we needed to attack them, which was in transition and with quick attacks. I thought we played pretty hard. We were just too slow in the first half."
With the Grizzlies trailing by 10, Conley said he decided to play more aggressively entering the fourth quarter to relieve the pressure on teammate Zach Randolph, whom the Spurs were double-teaming in the low post. Conley scored 12 points in the quarter, including 9 in the final 1:35 when the Grizzlies rallied from a 96-85.deficit. He added five more points in overtime.
"On the last play of the game I would have liked to have gotten it closer to the (3-point) line," Conley said. "But I had a good look."
The Spurs won their fourth straight road game and their seventh straight against the Grizzlies. San Antonio was playing its first game without center Tiago Splitter, who sprained his right shoulder in Saturday's win over the Clippers and is out for three to five weeks.
Memphis never led in the game until Conley connected on a 3-pointer with 2:25 to go in overtime for a 103-102 advantage. The Grizzlies also led 106-104 after newly acquired guard Courtney Lee hit a jumper with 1:27 to go, but Boris Diaw scored on a layup 25 seconds later and Duncan hit two free throws with 22.6 seconds left for a 108-106 lead.
The Grizzlies dropped to 0-9 against Southwest Division opponents.
The Spurs shot 57 percent in the first half and built a 53-41 lead. San Antonio was 23-of-40 shooting and Belinelli had 14 points. Duncan was 5 of 7 and scored 11 points.
The Spurs led by as many as 14 in the opening half.
Leading 25-22 at the end of the first quarter, the Spurs extended their advantage to 14 at 47-33 late in the second quarter and maintained a double-digit lead until the second half.
In the third quarter, the Grizzlies trimmed San Antonio's lead to 62-57 on a jumper by Conley, but the Spurs led by 10 entering the final quarter.
NOTES: Grizzlies guard Tony Allen missed his second straight game with a left hand contusion. ... The Grizzlies recalled guard Jamaal Franklin from the NBA Development League's Fort Wayne Mad Ants Tuesday. Franklin, the franchise's second-round draft pick a year ago, played one game for Fort Wayne and scored 15 points with four steals in 23 minutes. ... Lee, acquired from the Celtics as part of a three-team deal, made his debut and connected on his first shot, a 3-pointer in the second quarter. . . . San Antonio improved to a league-best 14-3 on the road this season. . . . The Grizzlies had won a franchise-record six straight overtime games before Tuesday night's loss.