Bryant, who rose above a defense-dominated contest with 28 points and eight assists, was shadowed by San Antonio's Kawhi Leonard and unable to get his hands on the ball after Green's clutch shot, forcing Pau Gasol to attempt a long three-pointer that ended their chances.
"I tried to keep the ball out of his hands because usually he hits the game-winning shot," Leonard said. "I wanted to let one of the other players shoot it."
The win was the third in a row for the Spurs (7-1), who got 19 points and seven assists from Tony Parker, as well as 18 points and nine rebounds from Tim Duncan.
The Lakers (3-5) had won their two previous games since coach Mike Brown was fired but are still waiting for his successor Mike D'Antoni to take over.
D'Antoni, who was named on Monday to replace Brown, is unlikely to make his debut until later this week because of recent surgery. His arrival should rejuvenate an offense that was held to a season-low total on Tuesday.
In a close battle throughout, San Antonio pulled 67-62 ahead early in the fourth before Bryant entered the game and ran off seven of the team's next nine points to tie the game at 71-71.
Bryant then assisted on three of the Lakers' final four field goals, playing the role of facilitator in the absence of injured point guards Steve Nash and his backup Steve Blake.
"When Steve (Nash) comes back I'm finishing plays (instead of starting them) which makes us more dangerous," said Bryant, who is anxiously awaiting his new coach and a full roster.
"It's not frustrating at all, we'll just wait."
Nash will eventually be reunited with the coach that helped him earn two league MVP Awards, but for now the current Los Angeles team fell to 2-1 under interim coach Bernie Bickerstaff.
San Antonio, meanwhile, is rolling along smoothly with a Western Conference-leading start.
Despite shooting just 39 percent from the field, San Antonio forced 17 turnovers from the Lakers and made it a war of attrition.
"We have been concentrating on our defense this year. We did a pretty good job of it," Spurs coach Gregg Popovich said.
"We're thrilled with the win."
Los Angeles, on the other hand, felt they let a game get away.
Dwight Howard finished with 13 points and 15 rebounds but found foul trouble while Gasol added 10 of each.
"I thought we had it in the box," Lakers forward Metta World Peace added.
"It was supposed to be 85-84."