Solid defense and experience in the clutch won out again.
"Memphis is a young, athletic, deep team," Spurs coach Gregg Popovich said. "They play everybody tough."
The Grizzlies weren't nearly so tough in their last visit here, when the Spurs rolled to a 109-89 win back on Nov. 28. This time, rookie O.J. Mayo and his teammates stretched the Spurs to the limit and had plenty of chances of their own to win.
"They know how to win," Mayo said. "Mostly at this point we're still learning how to win. Which is OK."
The Spurs have won five in a row and 11 of their last 13, with Parker leading them in scoring nine times during that stretch. San Antonio also got its third win of the season over Memphis.
Parker's two baskets put the Spurs up by four before O.J. Mayo hit a 3-pointer for Memphis with 71 seconds left. The Grizzlies had a chance to send the game into a third overtime when Mayo drove the lane in the final seconds, but he couldn't get off a clean shot. He dished to Rudy Gay, but Finley was able to swat the ball from behind on the layup and San Antonio's Roger Mason came away with the loose ball.
Kurt Thomas, who scored the Spurs' first basket of the second overtime, added a free throw for the last point with 0.5 seconds left on the clock.
"It was huge for us to get this win tonight," said Duncan, who was held to just five rebounds. "Tonight, we just found a way to win."
The Grizzlies, who snapped a four-game losing streak against Indiana on Friday night, fell to 2-12 on the road.
The Grizzlies held the lead in the final two minutes of regulation and took a quick lead at the start of the first overtime. Mayo was having fun, pulling up for long jumpers and one time bounced the ball off the back of the Spurs' Bruce Bowen before driving in for a layup.
Parker came to the Spurs' rescue every time. He scored their last seven points of regulation, gave San Antonio a 99-98 lead with a layup near the end of the first overtime and hit the two big jumpers in the second one.
"Tony stepped up and knocked down some big shots," Popovich said.
About the only thing he couldn't do was make a tough shot from deep in the left corner that would have won it in the final seconds of the first overtime.
Memphis had its late chances, too. Marc Gasol got to the free-throw line with 7.4 seconds left in the first overtime but missed his first shot before making the second to tie it at 99.
"I hope this game brings us closer as a team. I hope the pain draws us together," said Memphis coach Marc Iavoroni. "We're getting there, but we're not there."
Memphis had kept the Spurs off balance for most of the first three quarters. The Grizzlies held the biggest lead of the game at 57-46 in the third and up to that point, Parker, Duncan and Ginobili had scored all but six of San Antonio's points.
Defense and Duncan eventually got the Spurs back in the game.
With Parker and Bowen providing more pressure on the ball, the Spurs forced several missed shots and turnovers and start chipping away at the Memphis lead. Duncan scored nine points in the final 4:32 of the third and made it 66-66 going into the fourth with a baseline layup.
The Spurs are "a tested team," said Memphis' Hakim Warrick. "A championship team that's been through the wars."
The Spurs are 3-0 in double-overtime games this season. The Grizzlies have lost their two overtime games. ... The Spurs improved to 18-2 when scoring more than 90 points. ... Memphis outrebounded San Antonio 50-36.