With the Thunder pressing late in the fourth quarter, the Lakers made six consecutive free throws in the final 90 seconds and breathed a collective sigh of relief when Russell Westbrook missed a potential game-tying three-pointer in the final seconds.
All-Star guard Bryant was among six Lakers to score in double-figures, and added eight rebounds and six assists. He also survived a scare when he came down awkwardly on his left knee late in the fourth.
"I was scared. I did a lot of work with my flexibility and was able to bounce back but it was still scary," Bryant told reporters.
"We made adjustments after the first half, it's really about grinding it out and winning games."
Kevin Durant scored a team-high 30 points and Westbrook added 21 and 13 assists (13-14) for the Thunder, who slumped to their fifth loss in six games.
The league-leading Lakers (23-4) got off to a slow start in their first game back at home following a five-game road trip.
They trailed by 12 in the second quarter and were down by seven at halftime before their defense stiffened to capture the 16th win in their last 17 contests.
"Just getting ourselves back into the flow (after the road trip) took some time," said Los Angeles coach Phil Jackson.
"Oklahoma had been in L.A. longer than we were. Fortunately we had a good third quarter and played the way we anticipated we should."
It was the Thunder's 12th consecutive loss to Los Angeles.
(Editing by Peter Rutherford)