Steve Blake scored 23 points for the Lakers (44-37), who lead Utah (42-38) by 1½ games for the eighth postseason spot in the Western Conference after their seventh win in eight games even with Bryant watching from home following surgery on his torn Achilles tendon.
The Lakers weren't exactly relishing a future without their leading scorer, but they warmed to the challenge down the stretch.
"It definitely gives us confidence that if we play as hard as we did tonight, we can beat anybody," said Pau Gasol, who had seven points and 16 rebounds.
Bryant limped off the Staples Center floor Friday night, his 17th NBA season finished. He'll be largely immobile for the next few weeks, but he tweeted a plan to call in at halftime with adjustments for his teammates.
Most of the Lakers said they didn't actually hear from Kobe, but they knew he was proud.
"Whew!! Well done my dudes. Well done. UNO MAS (hash)playoffs," Bryant tweeted after the game.
The Lakers all shared Bryant's playmaking and defensive duties, working together imperfectly but effectively. Blake filled in for injured point guard Steve Nash and provided an unexpected scoring punch along with top reserve Antawn Jamison, who scored nine of his 15 points in the fourth quarter.
"We knew everybody doubted us, but that's fine," Howard said. "We're going to push even harder. I told our guys before the game, 'Nobody believes we can win. We've just got to go out there and play like it. We're all professional athletes. We've all done some great things in our career, so why not just go out there and play hard, and let everything happen?'"
Los Angeles blew open a tied game with a 15-4 run midway through the fourth. Bryant's starting replacement, Jodie Meeks, hit two 3-pointers during the rally, and Blake added three free throws in the final seconds while the Lakers fended off Tim Duncan's late rally for the Spurs.
The Lakers were clunky at times, with Gasol missing 12 of his first 13 shots and Howard struggling at the free throw line when San Antonio intentionally fouled him in the third quarter. They were still markedly effective, with a late-game smoothness they haven't often shown this season.
"Kobe is such a dominating player," Blake said. "He's going to have the ball in his hands, and we always want to play through him. Tonight, I think everybody felt they could show what they can do."
Los Angeles only needs one more win or one Utah loss to clinch its 16th playoff berth in Bryant's career. The Jazz visit Minnesota on Monday before finishing the season against Memphis, while the Lakers have the next two days off before their finale at home against Houston.
Duncan had 23 points and 10 rebounds for the Spurs, who have lost six straight road games. San Antonio (58-22) is likely to finish second in the West behind Oklahoma City (59-21), which holds the tiebreaker.
Tony Parker scored just four points on 1-of-10 shooting while playing for just the fourth time in April, possibly slowed by his injured shin in the Spurs' first game since waiving disenchanted forward Stephen Jackson. San Antonio is headed into another postseason as a top-two seed, but the Spurs have lost five of eight after failing to complete a season sweep of the Lakers.
"We didn't match their energy at all," San Antonio coach Gregg Popovich said. "I just thought we sort of floated through the game. Duncan was great, as usual. Timmy is a pro. ... He's really the only guy on the team that played like somebody who wanted to win a championship."
Duncan echoed Popovich's concerns about the Spurs' recent play while also expressing surprise at Popovich's decision to disrupt the team's chemistry by dumping Jackson so close to the postseason. Kawhi Leonard, whose increased prominence led to Jackson's dissatisfaction and dismissal, managed just eight points in 33 minutes against the Lakers, making only one field goal.
"We're two games away from the playoffs, and Manu (Ginobili) is still not here, Tony is still finding his rhythm," Duncan said. "We're not scoring at the rate we need to, but we're a veteran team, and we're confident we can get it together."
The Spurs couldn't have anticipated that the Lakers' biggest offensive surprise would be their backup point guard: Blake scored 14 points in the second quarter and hit four 3-pointers, fearlessly stepping up to create shots while Nash missed his seventh straight game with a right hamstring injury. Los Angeles is hoping Nash can return for the season finale.
NOTES: Blake outscored Parker 18-2 in the first half. ... The Lakers signed G Andrew Goudelock in time for the second-year pro to be in uniform. Goudelock was Los Angeles' second-round pick in 2011, and he showed enough scoring promise in 40 games of action last season to earn the nickname "Mini Mamba" from Lakers fans. He was waived in training camp last fall and spent this season with two NBA D-League teams. Goudelock would be eligible for the postseason if the Lakers make it. ... Charlize Theron, Edward James Olmos and Andy Garcia watched near courtside.