James also had 11 rebounds and four assists and finally got some much-needed help from his struggling All-Star teammates. Dwyane Wade scored 32 points, Chris Bosh had 20 points and 13 rebounds and the defending champions made sure the series will head back to South Beach.
Tony Parker had 15 points and nine assists while playing through a sore right hamstring for the Spurs, who were trying to move one step closer to their fifth championship.
Game 5 in the best-of-seven series is Sunday night in San Antonio.
Ray Allen scored 14 points for the Heat. Miami had 50 points in the paint after managing 32 in a 36-point loss in Game 3.
Tim Duncan scored 20 points, and Kawhi Leonard added 12 points and seven rebounds for the Spurs, who turned the ball over 19 times. After setting a finals record with 16 3-pointers in Game 3, San Antonio was 8 for 16.
James was an abysmal 7 for 21 for 15 points in Game 3, and he promised to be better in Game 4. He delivered on that the only way he knows how, hitting 15 of 25 shots and putting the team on his shoulders to set the tone early.
Every time James snatched a Spurs miss off the glass he thundered up the court, attacking the back-pedaling defense for easy layups that simply haven't been there for him this series.
He made six of his first seven shots, controlling the tempo and responding when the Spurs threatened to run away with the game in the first six minutes.
Parker strained his right hamstring during Game 3, leaving many in San Antonio to fear that the big step forward they made with their win in Game 3 came at a hefty price. But Parker deemed himself "ready to go" at the team's morning shootaround and looked fine, save for a quick trip to the locker room in the fourth quarter.
All the old Parker tricks were there in the first quarter -- a pull-up jumper to open the game, a driving layup and then another off the pick-and-roll. Leonard then buried a 3-pointer to give the Spurs a 15-5 lead early in the game.
Then James made the move the Heat have been waiting for all series.
He took the ball coast-to-coast on two straight possessions during run that tied it at 19. James then hit two mid-range jumpers -- an area that has been a struggle for him -- to cap the 14-2 surge and give Miami a 25-21 lead.
In an unusual move, Heat coach Erik Spoelstra decided to shuffle the starting lineup in the middle of a series. He inserted the sharp-shooting Mike Miller for big man Udonis Haslem in an effort to create more room for James and Wade to penetrate to the rim.
Miller was 9 for 10 on 3-pointers in his first three games of the finals, but was scoreless in the game.
Wade was averaging 2.7 points in the second half in the finals, but had eight in the third quarter of Game 4.
Wade then finished off the Spurs with a flurry of eight straight Heat points followed by an assist to Bosh for a 94-83 lead with seven minutes to play. The Heat's Big Three scored all but three points for Miami in the fourth.
If there was a common theme in the first three games, it was the curiously meek performance from James. He entered this series after perhaps the best season of his career, a versatile and efficient freight train that had taken the league and made it his own.
He was out to show just how far he'd come from 2007, when the Spurs dismantled his Cleveland Cavaliers in the finals and exposed the rising star as a player who could be neutralized if he was forced to settle for jump shots. James promised that he would not be so easily contained this time around, and .565 shooting percentage during the regular season, including .406 on 3-pointers, seemed to support that theory.
But the Spurs had done to him in these finals exactly what they did to him six years ago. They've clogged the paint with two big men -- Duncan and Tiago Splitter -- and surrounded him on the perimeter with a pack of hungry young wings led by Leonard and Green.
The results had been unlike anything the league has grown used to seeing from its biggest star. James entered Game 4 averaged 16.7 points on 38.9 percent shooting. He was just 3 for 13 from 3-point range in the first three games, and even more startling, only had six free throw attempts.
"I'm putting all the pressure on my chest, on my shoulders to come through for our team," James said. "That's the way it is."
It would be hard to find much higher stakes than Game 4 for the Heat. No team in NBA history has come back from a 3-1 deficit to win the championship.
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