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 3-for-21, including 1-for-9 from 3-point range.
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 had 12 points and Ginobili scored 10 for the Spurs. Ginobili shot just 3-for-13.
Two straight baskets by Bryant cut San Antonio's lead to three points with eight minutes remaining. Bowen made a 3-pointer with 7:38 left, but the Spurs went stone cold at that stage, going scoreless for nearly 6½ minutes.
The Lakers took advantage, scoring 10 straight points to take their first lead of the game. Bryant put them ahead for the first time by making two foul shots with 2:42 left, and added a jumper 24 seconds later following a turnover to make it 85-81.
The Spurs outscored the Lakers 14-2 to start the third quarter for a 65-45 lead, drawing groans from the crowd of 18,997 at Staples Center, where the Lakers haven't lost since March 28.
Suddenly, the Lakers came together, scoring 14 straight points in a span of 3:05 to draw within six. Bryant had seven points and two assists during the run.
Ginobili's 3-pointer ended a four-minute scoreless drought, and the Spurs led 72-65 entering the fourth quarter.
Duncan dominated the inside in the first half, getting 16 points and nine rebounds as the Spurs took a 51-43 lead.
Shadowed by Bowen wherever he went, Bryant scored only two points in the half, making one of three shots and going without a free throw. He averaged 33.3 points and 13.4 attempts from the foul line in the Lakers' previous 10 playoff games. Lakers coach Phil Jackson joked after the third quarter that Bryant had been on vacation.
Backcourt mate Derek Fisher, averaging 11.9 points in the playoffs, went scoreless until the fourth quarter, when he scored four.
Radmanovic, averaging 8.2 points in the postseason, made five shots without a miss for 10 points in the first quarter, but didn't attempt a shot after that.
Notes: The Lakers are 52-7 when winning Game 1 in a best-of-seven series. ... The Lakers have beaten the Spurs in seven of their previous 10 postseason matchups, including all three in the conference finals. ... The teams are meeting in the playoffs for the sixth time since 1999, but the first since 2004, when the Lakers prevailed in six games in the conference semifinals. The Lakers didn't win a postseason series from 2005-07. ... Lakers coach Phil Jackson has an NBA-record 188 postseason wins, while San Antonio's Gregg Popovich has 100, tied for the third-most in league history with Larry Brown. Pat Riley is second at 171. ... Jackson-coached teams are 40-0 when they win the opener of a seven-game series. ... San Antonio's Robert Horry has won seven championship rings - two with Houston, three with the Lakers and two with the Spurs. ... The Lakers have won 17 of their last 19 Game 1 home playoff games, and 19 of their last 22 home playoff games overall.