Sacramento fell to 1-17 against Miami since March 2004.
James was perfect in the second overtime: 3-for-3 from the field, 4-for-4 from the line. He had more points (11-5), rebounds (3-0), and assists (3-1) in the final five minutes than the Kings had combined.
"No matter what their record is, they made plays just like us. They gave everything they had and more," James said.
The Heat missed key free throws late in both regulation and the first overtime — Wade missing a pair with 21 seconds left in the fourth, and James missed one of two with 29.3 seconds left in the opening extra session.
Those two free throws were the only ones Wade was awarded all night.
"I knew we came out a little flat and they came out so free," Wade said. "So I told myself to be a little aggressive and kept us afloat a little bit. And in the overtime, LeBron got going a little bit. We kept going to him and he delivered."
In the first OT, the Kings had a chance for the late lead and potentially the win, but Thomas had a layup blocked by Bosh, and Allen grabbed the rebound for the Heat with 5.7 seconds left.
Miami put the ball in Wade's hands, and he found James near the basket. James' shot missed, and he complained he was fouled by Salmons on the attempt. Referees disagreed with that, but after a lengthy review to determine possession, they awarded Miami the ball with 0.4 seconds remaining. It was much ado for nothing, as Bosh's shot sailed long and the teams went to double overtime.
The game was tied at 92 midway through the fourth before Wade — with six points and an assist — led a 13-4 run that looked like it would give Miami breathing room. Miami was up 105-96, and still led 112-104 when James scored with 1:40 remaining.
Sacramento roared back, scoring the final eight points of regulation. Thornton hit a pair of 3-pointers, the second coming with 23 seconds left to get the Kings within 112-110. And after Wade missed a pair of free throws, Cousins grabbed an offensive rebound and laid it back with 8.5 seconds remaining to knot the game at 112-all.
Out of a timeout, the Heat went to Wade, whose step-back 20-footer bounced off the rim as time expired, sending it to overtime.
They were just getting started. And when it was over, the Heat streak survived.
"We're coming together," James said. "We're doing it the right way. We're executing offensively. We're sharing the ball. And we're not getting rattled. We've been in some crazy games. We just stay the course and figure out a way to get the victory."
NOTES: Miami finished February with a 12-1 record, with the one loss to start the month. ... The Heat have allowed 68 third-quarter points in their last two games, both at home. They gave up 67 third-quarter points in their previous three games, all on the road. ... One day after celebrating his 24th birthday, Kings G Jimmer Fredette did not play. ... The Heat played without F Shane Battier, sidelined by right hamstring tightness. He's day-to-day.