SAN ANTONIO — Miami Heat owner Micky Arison had a message as he walked to the winning locker room.

“The death of the Big Three was overrated,” he said.

Sure was. LeBron James, Dwyane Wade and Chris Bosh, his three prized players, are just fine.

So are the Heat’s championship hopes.

Riding big performances from their three All-Stars, the Heat tied the NBA Finals with a 109-93 victory over the San Antonio Spurs on Thursday night in Game 4.

“It was on our shoulders,” James said. “We had to figure out how to win the game for us and play at the highest level. When all three of us are clicking we’re very tough to beat.”

James had 33 points and 11 rebounds after failing to break 20 points in any of the first three games of the series, and Wade scored 32 points, 11 more than his previous high this postseason.

Bosh matched his playoff high with 20 points and grabbed 13 rebounds, he and Wade supplying the baskets that finally put the Spurs away for good midway through the fourth quarter.

Three players, 85 points. Just the way the Heat envisioned it when they signed James and Bosh to play with Wade in 2010.

“When Bosh, Wade and James score the way they did tonight and shoot it the way they did tonight, a team is going to have a difficult time if you help them like we did,” Spurs coach Gregg Popovich said.

“When those guys are playing like that, you better be playing a perfect game.”

The Spurs weren’t, committing 19 turnovers that led to 23 points.

And just like they have for the last five months, the Heat bounced back from a loss with a victory. They are 12-0 after defeats since Jan. 10, outscoring opponents by an average of nearly 20 points in the previous 11 victories.

Tim Duncan scored 20 points for the Spurs, who have one more game here on Sunday. They fell to 10-3 at home all-time in the finals, failing to back up their 113-77 victory in Game 3 that was the third-most lopsided score in the history of the championship series.

James insisted he would be better after shooting 7 of 21 from the field with no free throws in that game, saying he was the star and it was his job to lead his team. He was 15 of 25 on Thursday.

But while James — and millions of critics worldwide — wanted to pile all the pressure on the league’s MVP, it was Wade on Wednesday who said it was the Heat’s three All-Stars who had to lead them together, or there would be no championship.

He was right. And now those championship hopes are right back on track.

“It was all about myself, Chris and LeBron coming out and leading this team to a victory,” Wade said.

“The thing we talked about is we all have to make an impact in this game, somehow, some way.”

Wade shot 14 of 25, adding six steals, six rebounds and four assists in a performance that James compared to when Wade was MVP of the 2006 finals.

Tony Parker had 15 points and nine assists for the Spurs, who made a finals-record 16 3-pointers on Tuesday but got up only 16 attempts in this one. Gary Neal scored 13 points and Danny Green had 10, solid nights but nothing like when they combined for 13 3-pointers two nights earlier.

“They play very aggressive defense,” Parker said. “They gamble and they take a lot of chances, and tonight it worked.”

The Heat guaranteed they will get at least one more game on their home floor. Game 6 will be Tuesday night, where they could have a chance to celebrate a second straight championship.

The revelry in south Florida was marred Thursday by an accident in which the deck behind a popular sports bar collapsed during the game, spilling patrons into Biscayne Bay. Miami Dade Fire Chief David Downey said 24 people were transported to area hospitals, and that two people were in serious condition.

“We share our concerns for all that was injured at Shuckers restaurant,” Wade said as he started his postgame news conference.

Wade, battling right knee pain throughout the spring, helped the Heat put it away in the fourth quarter. He followed a basket with a steal and dunk, pushing the lead to 90-81, and after he made another jumper, Bosh scored the next six Heat points, taking the load off of James.

“We’re not going to put him on an island,” Bosh said. “He’s never alone. We’re out there with him.”

The Heat switched their lineup, inserting Mike Miller, who made 10 of his 11 shots, going 9 of 10 on 3-pointers, in the first three games of the series. They changed uniforms, too, switching from their road reds to their blacks.

The only change they really needed was in the performances of their Big Three.

James called it a “must-win” and it probably was: No team has overcome a 3-1 deficit in the finals.

And the way their three stars played, they couldn’t lose.

The Heat blocked shots, made stops, and occasionally flopped, playing with renewed aggression after what coach Erik Spoelstra called a “miserable” day of watching and analyzing their passive performance from Tuesday.

They still haven’t lost two in a row since Jan. 8 and 10.

Parker played through a strained right hamstring, shooting 7 of 16, but the Spurs couldn’t match the Heat’s speed.

After the teams traded blowouts in the previous two games, momentum swung wildly in a first half that ended tied at 49. San Antonio raced to a quick 10-point lead, fell behind by 10 with 7 minutes left in the half, then finished with an 11-2 spurt sparked by reserve Boris Diaw. Bosh dove for a dunk that came just after the buzzer, Spurs owner Peter Holt waving it off from his seat along the sideline.

James rocked back and forth during the national anthem, a bundle of energy ready to get going. It took a few minutes after the game started, but he began playing with the speed and power that can make him unguardable, grabbing rebounds on defense and rushing the ball up the floor himself to get the Heat into their offense.

He and Wade combined to make 10 of 11 shots and score 21 points in the first quarter, helping the Heat erase their early 10-point deficit to go ahead 29-26.

Popovich even lit into Duncan during an early second-quarter timeout with Miami on its way to a 41-31 advantage, but the Spurs had it back to even by the time the teams headed to the locker room.

Notes: Sebastien De La Cruz, an 11-year-old mariachi singer, sang the national anthem again after his Game 3 performance set off a barrage of racist tweets by what Popovich called “idiots.” Popovich and Spoelstra congratulated him at midcourt after his performance, which earned him a rousing ovation. … James passed Hakeem Olajuwon (3,755 points) and John Havlicek (3,776) to move into ninth place in career playoff scoring. James has 3,777. James has 3,777.