SALT LAKE CITY -- The final result remained the same, but at least the Utah Jazz made their latest loss to the San Antonio Spurs a competitive game.

Kawhi Leonard hit a late game-winning shot and the Spurs held off a furious comeback for an 88-86 win over the Jazz on Tuesday.

San Antonio had won the three previous contests this season by an average of 26.7 points.

"They played with a lot of energy," Spurs coach Gregg Popovich said of the Jazz. "They're very aggressive. I thought they moved the ball much better than we did. We were very lucky to win. They actually played better basketball tonight than we did."

Not when it mattered most, though.

Leonard scored 18 points, but none were more clutch than the mid-range jumper he sank to beat the shot clock with 4.9 seconds remaining.

LaMarcus Aldridge and Manu Ginobili added 14 points and Tony Parker and Kyle Anderson each chipped in 11 as the Spurs improved to 65-12 with their fourth straight victory.

Tim Duncan only had three points, but registered his 1,000th career NBA victory. He became only the third player in NBA history to reach that milestone in the regular season, joining Kareem Abdul-Jabaar (1,074) and Robert Parish (1,014).

"Amazing," Parker said of his Hall of Fame-bound teammate. "The longevity. Playing at a high level every game for 19 years. Pretty impressive. Speaks for itself. Unbelievable."

The Jazz, fighting for their first playoff appearance since 2012, looked outmatched early in the fourth quarter before fighting out of a 16-point deficit to take a late lead.

Rodney Hood scored 23 points, including 13 in the fourth-quarter rally. The second-year shooting guard had a chance to win the game, but his step-back 3-pointer bounced off the front of the rim and time ran out on the Jazz's comeback.

"It felt good," Hood said. "They got a good contest on it. I don't know who ran out on me. When it left my hands, it felt good. The shot I took, I'll live with it."

Joe Ingles and Shelvin Mack each scored 13 points and Gordon Hayward had 12 as Utah fell to 39-39. The Jazz, now in the eighth spot in the Western Conference, are a half-game ahead of Houston and a half-game behind Dallas with four remaining.

The game looked over early in the fourth quarter after the Spurs went on a 19-4 run and took a 69-53 advantage after a Danny Green layup.

Ingles, a backup small forward, sparked a huge comeback for the Jazz, hitting three 3-pointers and scoring 11 points in the fourth quarter.

"Joe came in and gave us a huge lift," Jazz coach Quin Snyder said. "I thought our defense helped us stay in it until we could hit a few shots."

Hood also lit it up in the final period as Utah attempted to avoid a four-game season-series sweep with a potential playoff opponent. Hood gave the Jazz their first lead, 84-83, since the first quarter with a minute remaining.

The final minute was an entertaining back and forth exchange.

Parker answered Hood's go-ahead bucket with a 3-pointer, but Hayward tied it back up on the Jazz's ensuing possession.

Rudy Gobert, who had 10 rebounds, four points and two blocked shots, swatted a Parker attempt with seven seconds to go. The Spurs called a timeout and Leonard answered with the game-winner on an assist by Anderson.

"The first option was (Aldridge)," Parker said. "They played good defense on LA, so we went to the second option. Obviously, Kawhi is a great option, too."

Utah took an 18-12 lead in the first quarter before things went awry. The Spurs went on a 19-2 run and took a 42-37 lead into the break.

This was the Jazz's first loss all season in 27 tries when holding an opponent under 90 points.

NOTES: Gregg Popovich was asked which players he planned to play against the Jazz. The Spurs coach pointed to the visitors' locker room behind him and joked, "The guys in the black uniforms. There's a list somewhere. You should check it out." ... Popovich also had a humorous response to a question about how he has changed over the years as a coach. "I take things in stride a lot better," he said. "I don't watch as much film as I used to. I learned that from Jerry Sloan. At one point, somebody asked him, 'Do you watch film?' (Sloan said), 'What would I watch film for? That's what I have assistants for.' I'm more like Coach Sloan now in that respect." ... The Jazz announced Monday that they are relocating their D-League affiliate, the Idaho Stampede, to Salt Lake City in time for the 2016-17 season. The team's new name will be the SLC Stars, an homage to the 1971 ABA champion Utah Stars.