After two falls, Wise got it right at the third time of asking, scoring 97.20 in the final round to push compatriot Alex Ferreira (96.40) into second place.
Sixteen-year-old New Zealander Nico Porteous claimed the bronze medal with a score of 94.80.
Ferreira, who scored more than 90 points in all three runs, led going into the final round but Wise, who had failed to go clean on his first two attempts, delivered four double corks to match the gold he won when the event made its debut in Sochi.
With six of the top 10 skiers in the World Cup rankings hailing from the United States, many had predicted an All-American podium sweep.
However, Porteous had other ideas as he produced a stunning second run that belied his age to secure New Zealand's second bronze medal of the day.
Fellow 16-year-old Zoi Sadowski-Synnott won New Zealand's first Winter Olympics medal since 1992 earlier on Thursday morning in the women's snowboard big air.
Speaking to reporters after the final, Wise blamed faulty bindings for the two uncharacteristic falls leading up to the winning final run.
"I honestly feel like I had three great runs today," said the 27-year-old.
"My first run was shaping up to be one of the best runs of my life and then all of a sudden I was down. In the transition, the ski came off uncharacteristically. The same thing happened on the second run."
"For run three, we cranked my bindings up as high as they go," he added.
"My leg is coming off before my ski does. I dropped in and I knew first of all that I had to make it happen and second of all that I could."
Wise managed to top a world-class field through being the only man capable of landing four different double corks in the same run.
"Everybody here can do one of those four tricks. They all have one of them in there, so they are not that hard," stressed Wise.
"I am not going to say that all of my tricks are the hardest in the game but putting all four of them into a run is certainly the most challenging thing I have ever done in my life.”
Porteous produced the run of his young life to step on the podium alongside the two Americans.
After laying down a second run to move into second place, he then decided just to ride down the pipe and not attempt any tricks in the final round, shouting out "can't do better than that" as he reached the bottom.
His score was enough to secure the bronze medal and the teenager said he just had nothing left to give in the final round.
"I had nothing left. That was me. That was all I had left in the bag," said the Kiwi.
"I hope people don’t see it as me being cocky. I had nothing left. It was the best run of my life, hands down."
His compatriot Beau-James Wells finished an admirable fourth, after seeing his brother Byron crash-land during practice and pull out before the start.
A New Zealand team spokesman confirmed Byron had suffered a knee injury.
(Reporting by Jack Tarrant; Editing by John O'Brien/Amlan Chakraborty)
