Instead, the Sacramento Kings spoiled those plans -- and James hurt himself in the process.
"I thought our guys accepted the challenge," Sacramento coach Michael Malone said.
James said he strained his right groin before finishing with 33 points, eight rebounds and eight assists as Miami's six-game winning streak ended. Whether he plays at Portland on Saturday night is uncertain.
"It ain't feeling too good right now," James said.
The two-time defending NBA champions played without Dwyane Wade (resting his knees), Ray Allen (right knee tendinitis) and Chris Andersen (sore back). James stayed mostly on the perimeter in the second half when his injury started to swell.
The Kings capitalized on the opportunity.
Isaiah Thomas had 22 points, 11 assists and seven rebounds to help Sacramento (9-19) upend the Heat (22-7) a week after a blowout loss in Miami. Gay made a tying jumper in the final minutes of regulation, and the Kings quickly pulled away in the extra period to bring the sellout crowd of 17,317 roaring to its feet.
"This is a new team, and for us to come out and perform against one of the best teams in the league, it's a pretty good feeling," Cousins said.
Malone had even called out his players' mistakes publicly following a loss to New Orleans on Monday. He gave his players a couple of days off around Christmas and asked them, "What type of team do we want to be this season?"
"The biggest thing is we responded," Gay said.
The Kings overcame 23 turnovers and some lackluster defense at the start to pull off the comeback. Sacramento outshot Miami 49.4 percent to 44.2 percent and outrebounded the Heat 51-35.
A day after winning The Associated Press' 2013 Male Athlete of the Year, James helped the Heat build a big lead early but couldn't hold off a late Kings rally by himself. He also tweaked his left ankle when he fell into the crowd after missing a layup in the second quarter.
James set up Chris Bosh for a dunk, then made one of two free throws to put the Heat ahead 89-85 with 2:42 remaining in the fourth. A few plays later, Mario Chalmers was called for a flagrant foul after pushing Cousins to the ground. Cousins made both free throws, and Gay hit a tying turnaround jumper.
After Gay forced a turnover by James, Thomas missed a running shot. James came down with the rebound, dribbled down court and missed a difficult 3-pointer over Gay at the regulation buzzer.
Gay made a 3 and Thomas hit a pull-up shot at the start of overtime. After James made a driving layup, Thomas answered with another from beyond the arc to give the Kings a 97-91 lead.
James still nearly rallied Miami from eight points down in the final minute. He hit three consecutive 3-pointers -- sandwiched between Sacramento scores -- to bring the Heat within three with 13.1 seconds left.
But James and the Heat simply ran out of time.
At the outset, James wasted no time putting Miami in control. He scored nine points and assisted on two of Shane Battier's three 3-pointers during a 23-6 run to open the game.
With James on the bench, Sacramento sliced Miami's lead to seven in the second quarter. The four-time NBA MVP returned and restored order -- at least for a moment -- to help the Heat go ahead 55-45 at halftime.
The Kings outscored Miami 29-18 in the third quarter behind big plays from Cousins and Gay -- with almost all of them directed by Thomas. Sacramento entered the fourth with a 74-73 lead to set up a furious finish.
"The game turned in the third quarter," Heat coach Erik Spoelstra said. "Probably more than anything our offense got us in trouble. A lot of jump shots. And they stepped up their defense. You have to give them credit for that."
James passed Larry Bird (21,791 points) and Gary Payton (21,813 points) to move into 29th place on the NBA's career scoring list. ... Spoelstra said Greg Oden's rehabilitation from various knee injuries is progressing, but the center is not expected to play in Miami's lone visit to Portland on Saturday night. ... Cousins was called for his NBA-leading ninth technical foul after arguing with officials in the first quarter. ... The Heat entered with a 7-0 record against Western Conference teams this season.