San Antonio captured the NBA title with one game to spare as they overcame New Jersey 88-77 to take an unbeatable 4-2 lead in the finals.
For much of a thrilling game, the championship appeared headed for a decisive seventh game - but the Spurs hit back deep into the final quarter.
Tim Duncan, who was awarded the Most Valuable Player award, top-scored with 21 points and Stephen Jackson sparked a run of 19 points in a row as San Antonio made their late rally.
"These guys didn't want to go home. They didn't want to give up," Duncan said.
"Give a lot of credit to our guys. They stayed the whole way through."
The loss has no bearing on what I will decide... but this is my second time to fall short
Nets star Jason Kidd on his future plans
It was the second successive Finals defeat for New Jersey, who were swept aside by the Los Angeles Lakers last year.
Duncan added 20 rebounds and 10 assists while Jackson had 17 points and David Robinson, playing the final game of his 14-year NBA career, had 13 points and 17 rebounds.
Jason Kidd led the Nets with 21 points.
The Nets led 72-63 after a Rodney Rogers three-pointer with 8:54 remaining, but the Spurs, who had not led up until that point, scored the next 19 points as New Jersey went 5:34 without a point.
Former Nets guard Jackson sank back-to-back three-pointers to give his side the lead and then sent the home crowd into a frenzy with a third on the run.
Kidd, in what could be his last appearance for the Nets, made a pair of late baskets but it was too late for his side.
Kidd is a free agent - and San Antonio is thought to be his most likely destination.
"The loss has no bearing on what I will decide," Kidd said.
"But this is my second time to fall short. I've got to find a better team, or stay with the Nets, to find a way to win a championship. That's what I'm playing for."