How the Lakers won Tuesday was a mystery with their six-for-22 shooting in the fourth quarter at Staples Center.
Bryant had 32 points and moved to within 31 of passing Jordan for third on the NBA's all-time scoring list.
He seemed to be feeling every one of his 32,262 career points, wincing and grabbing his back throughout Tuesday's game.
"Yeah, absolutely. I'm hurting," he said.
Bryant could pass Jordan in San Antonio on Friday or Sunday at Minnesota.
In the final five minutes against Sacramento, Bryant found Wesley Johnson for a three-pointer, dunked after a fastbreak pass from Jordan Hill, set up Hill for a layup and made all four of his free-throw attempts.
"We got the right stops and we got it to our closer, Kobe, who made big free throws, made big plays, was a great playmaker tonight," said Carlos Boozer, who had 15 points and nine rebounds in his second game as a reserve.
A loss would have been especially troubling for the Lakers (6-16) because DeMarcus Cousins, the Kings' leading scorer and rebounder, sat out while recovering from viral meningitis.
"Less lottery balls!" said center Robert Sacre, a response to Johnson's view that the Lakers should keep losing. "No one wants to hear that. We're not trying to tank."
Lakers Coach Byron Scott said Bryant could see more time at point guard, particularly after Lin and Price each made one of five shots. Bryant had six assists, as did Price, while Lin had four in front of 18,267, the Lakers' first non-sellout crowd at home this season.
Several Lakers, including Bryant and Lin, wore black-and-white "I Can't Breathe" T-shirts during pregame warmups and while on the bench during the game.
It mirrored the actions of other NBA players, notably Cleveland's LeBron James, and was a sign of support toward Eric Garner, who died in July after being placed in a chokehold during an arrest. Garner could be heard gasping "I can't breathe" to the police officer in a video recording.
Bryant arranged for the shirts to be worn by the Lakers.
Follow Mike Bresnahan on Twitter @Mike_Bresnahan