Meanwhile, the San Antonio Spurs steamrolled into the NBA Western Conference finals after a 102-99 win over the Los Angeles Clippers gave them a clean sweep of their seven-game series.
The Heat, who struggled in their previous games after Chris Bosh was ruled out with an abdominal injury, trailed by eight points at half-time but snatched the momentum when James and Wade took control in a dominant third quarter.
"This is what the play-offs are all about. It's just survival," said Heat coach Erik Spoelstra.
James, named last week as the NBA's Most Valuable Player, scored 40 points, with 18 rebounds and nine assists.
Wade, who was subdued in Game Three, responded with 30 points, nine rebounds and six assists as the Heat sparkled in a stunning return to form.
"Me and 'Bron had it going," said Wade. "We played off of each other very well.
"We both were aggressive at the same time. That's beautiful basketball for the Miami Heat when we play that way."
Forward Danny Granger led Indiana with 20 points but the Pacers were powerless to curtail James and Wade in a rampant third quarter.
"You get the ball out of one of those guys' hands and it just gets to the other guy's," lamented Pacers coach Frank Vogel.
The Pacers led 54-46 at half-time but James and Wade put the visitors in front when they combined to score the first 28 points for the Heat, who went on a 25-5 run.
"We had a terrible performance in Game Three," said James. "We wanted to redeem ourselves."
The teams return to Florida for Game Five on Tuesday.
"It's still going to be a dogfight," James said. "It's a three-game series now."
Elsewhere, the West's top seeds rolled to their 18th consecutive victory, going back to the regular season, as the Clippers fell to the same fate as the Utah Jazz in the first round, exiting the play-offs after being swept 4-0.
Sunday's game was tight, and San Antonio trailed by one with two and half minutes remaining, but Tony Parker answered with a pair of clutch baskets and the visiting Spurs showed the nerve that has seen them dominate the NBA over the past month.
"We needed a game like that," Parker said. "That was a great game for our young guys to get some experience. At the end of the game we executed our plays and made big baskets."
Tim Duncan scored 21 and Parker finished with 17.
The Clippers' Chris Paul recorded 23 points and 11 assists, but he committed a turnover and missed a potential game-tying shot on two of his team's final possessions.
Mo Williams failed to get a final desperation shot off as the Staples Center crowd fell to hush and the Clippers saw their season come to a close.
San Antonio's post-season march is in contrast to last year when they were stunned in the first round as top seeds.
It also has them positioned to make a run at their first NBA title since 2007.
"I know how good this team was last year, and we're healthier and deeper," said guard Danny Green, who finished with 14 points. "I know what we're capable of."
San Antonio will play either Oklahoma City or the Los Angeles Lakers for the Western Conference title.
The Clippers, playing in the second round of the play-offs for the first time since 2006, were outclassed in every department by the seasoned Spurs.
A day earlier, Los Angeles squandered a 22-point advantage to lose Game Three, but this time they fell behind by 12 in the second quarter but fought to make it a test.
Reserve guard Eric Bledsoe scored 10 consecutive Clippers' points in the fourth, he had 17 on the night, to help give the home team a five-point edge with five minutes left but the Spurs battled back.
With Paul and Blake Griffin, who had 21 points, the Clippers have every reason to be optimistic for the future.
"I told them 'this should hurt,'" said Clippers coach Vinny Del Negro. "More is expected, and that's a good thing."