Game 2 will be played Friday night before the best-of-seven series shifts to San Antonio for the third and fourth games. The Lakers are 7-0 in the postseason at Staples Center, where they've won 13 straight games overall.
Bryant's jumper put the Lakers ahead for good after two free throws by Manu Ginobili with 1:22 remaining and a follow shot by Tim Duncan with 41 seconds left tied the game at 85. Ginobili then missed a 3-pointer, and Sasha Vujacic made two free throws with 7.3 seconds remaining to complete the scoring.
The Lakers outscored the Spurs 24-13 in the fourth quarter, when San Antonio shot 4-of-18.
Bryant also had five rebounds and nine assists. Pau Gasol had 19 points and seven rebounds, and Vujacic and Vladimir Radmanovic scored 10 points apiece for the Lakers.
Duncan led the Spurs with 30 points, 18 rebounds and four blocked shots. Tony Parker added 18 points, 10 rebounds and six assists, Bruce Bowen scored 12 and Ginobili added 10 for the Spurs. Ginobili shot just 3-for-13.