The Lakers slipped to 0-3 after James, who joined the LA franchise this summer, missed with a potential game-winning three-pointer with less than three seconds to go.
James had landed a 3-pointer with 3.3 seconds of regulation time left to take the game into overtime after the Lakers had trailed by eight points with 70 seconds remaining.
But with the Lakers up by one with 13 seconds left in the game, James missed two free throws and he could not respond after Patty Mills had put the Spurs ahead with seven seconds left.
The Lakers were missing Brandon Ingram and Rajon Rondo, who were both suspended for their part in the melee during the defeat to the Houston Rockets.
Kyle Kuzma stepped up with 37 points while James ended with 32, but LaMarcus Aldridge’s 37 points and 10 rebounds helped the Spurs improve to 2-1.
The Golden State Warriors bounced back from their defeat on Sunday night with a comprehensive 123-103 victory against the Phoenix Suns.
Stephen Curry hit six three-pointers in his 29-point performance while Kevin Durant added 22 for the reigning NBA champions.
The Toronto Raptors are 4-0 after easing past the Charlotte Hornets 127-106.
Kawhi Leonard top-scored with 22 points for the Canadian side, who have earned three of their wins by a margin of more than 10 points.
Kyle Lowry added 16 points and 14 assists as every Toronto player who took to the floor scored some points.
The Boston Celtics, pre-season favourites in the Eastern Conference, fell to 2-2 after they were beaten 93-90 by the Orlando Magic.
Nikola Vucevic had 24 points and 12 rebounds for Orlando, who bounced back from two successive defeats to improve to 2-2.
Celtics duo Kyrie Irving and Gordon Hayward both had three-point attempts in the final seconds but neither were able to force the game into overtime.
The Milwaukee Bucks moved to 3-0 after seeing off the New York Knicks 124-113, with Giannis Antetokounmpo recording a 31-point haul and claiming 15 rebounds, while the Minnesota Timberwolves were 101-91 winners against the Indiana Pacers.
The Washington Wizards spoiled the Portland Trail Blazers’ night as the visitors won 125-124 after overtime.
Portland’s players had turned up for the game in Halloween costumes but they were unable to mark the evening with a victory in a thrilling finale.
John Wall missed two free throws for Washington with six seconds left but Damian Lillard’s attempted game-winning shot was blocked by Otto Porter Jr.
Elsewhere, Zach LaVine’s 34 points were in vain as the Chicago Bulls were beaten 115-109 by the Dallas Mavericks while the Memphis Grizzlies saw off the Utah Jazz.
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