SAN ANTONIO -- If nothing else was learned from the San Antonio Spurs' ragged, rugged 95-89 overtime win over the Memphis Grizzlies on Tuesday night at the AT&T Center, one thing is surely understood -- a seven-game playoff series between the two teams would be a battle.

Kawhi Leonard scored 32 points, grabbed 12 rebounds and took charge of the game at the free-throw line in the final seconds to help lift the Spurs to a victory.

This was a game that started out as dreadful (Memphis led 16-14 at the end of the first quarter and 35-33 at halftime) and finished with both teams hitting huge shots in the final minute of regulation before San Antonio prevailed.

If the playoffs started today, the Spurs (60-17) and Grizzlies (42-36) would play in the first round. Both teams would be well served to stock up on extra smelling salts and athletic tape now.

The game was tied at 86 with 2:15 left in overtime before Pau Gasol and Patty Mills hit 3-pointers on consecutive possessions to give San Antonio the lead for good. Leonard sealed it by making three free throws in the final minute.

The lead changed hands three times in the final minute of regulation until an alley-oop layup by San Antonio's LaMarcus Aldridge off a perfect inbounds pass by Pau Gasol with 1.6 seconds to play tied the game at 84 and forced overtime.

"Anytime you have to make plays down the stretch and you are behind and to execute it's good for the team and good for your confidence," Leonard said. "Both teams were making shots the end. They pack the paint and don't allow you to get easy layups and get their hands on a lot of balls.

The victory was the third in a row and eighth in 10 games for the Spurs (60-17), who still have a mathematical chance to snatch the best record in the NBA from Golden State, which leads San Antonio by 3 1/2 games. San Antonio has five games remaining, the Warriors four.

San Antonio reached 60 wins for the second straight season and seventh time in franchise history. It is third best all time in the NBA history, behind Boston (13) and the Los Angeles/Minneapolis Lakers (11).

Aldridge added 15 points for the Spurs while Pau Gasol chipped in 12 points and 11 rebounds and Tony Parker and Mills had 10 points each for San Antonio.

Mike Conley led the Grizzlies (42-36) with 19 points and Zach Randolph added 18 points and took 16 rebounds for Memphis. Marc Gasol contributed 11 points and Troy Daniels and Wayne Selden scored 10 points apiece for the Grizzlies.

"This was a game we wanted to send the message that we are not going to lay down at the end of the year," Conley said. "We're frustrated with the loss. We are team that continues to push. Playing the Spurs is always a dogfight, and if we get to play them in the playoffs we understand what to expect. They played this game like it was a playoff game. It was good lesson."

Added Memphis coach David Fizdale: "I do like how we scrap. That's who we are. We really competed but again, the mental errors against this team destroy you. Every single breakdown, every miscommunication, every poor decision you make, the Spurs counter it."

Leonard and Conley both went to the floor with 3:42 remaining after inadvertently clashing heads under the Grizzlies' basket. Both players got up under their own power but Conley had to leave the game with blood gushing from a cut on his right eyelid. The gash required a continuous stich to close and Conley did not return.

"Memphis is really physical and it bogs us down offensively," Mills said. "For us to counter that we need to do our job defensively and run out of that, get rebounds and flow into our offense. We want to get better in all aspects of the game. It was good to get that matchup."

NOTES: Memphis G/F Tony Allen missed the game with a left eye injury while the Spurs were without Gs Danny Green (left quad contusion) and Dejounte Murray (left groin). It was the 12th straight game Murray missed. ... Spurs G Manu Ginobili left the game early in the second quarter with a right quad contusion and did not return. ... Grizzlies C Marc Gasol and Spurs F/C Pau Gasol started opposite each other in the 2015 NBA All-Star Game, becoming the first pair of brothers to start the same All-Star Game and the second brothers to play in the same NBA All-Star Game (Tom and Dick Van Arsdale in 1970 and 1971).