Hocker outsprinted defending champion Jakob Ingebrigtsen of Norway and Britain's world champion Josh Kerr to take gold in an Olympic record of 3min 27.65sec.
"That's an unbelievable feeling," said Hocker. "My body just kind of did it for me. My mind was all there and I saw that finish line.
"Winning gold was my goal this entire year. I wrote that down and I repeated it to myself even if I didn't believe it.
"My performances showed me that I was capable of running 3:27, whatever it took. I knew I was a medal contender, and I knew that if I get it right, it would be a gold medal. I've been saying that."
Hocker said he was happy to have flown in relatively unnoticed.
"I told myself that I'm in this race, too. If they let me fly under the radar, then so be it. I think that might've just been the best," the American said.
Kerr bagged silver in a national record of 3:27.79, while Ingebrigtsen came fourth after being passed by another American, Yared Nuguse, who clocked a personal best of 3:27.80.
"No and yes," was Ingebrigtsen's response when asked if he'd employed the wrong strategy.
"Of course it's a tactical error that I'm not able to reduce my pace over the first 800," he said.
"It's just a little too hard but I think I saw in the back straight with 650 to go that they were opening a little bit of a gap. I tried to respond by going just a little bit too much on the gas. It was just 100 metres too much."
Kerr said that his "ears and legs are gone".
"I'm proud of the performance I put out there today," Kerr said. "I said to myself I'll control my controllables, I did that today.
"I executed the fastest that I've ever run by almost two seconds. It wasn't enough. That's sport.
"I left no stones unturned and that's the result today. Of course, I was looking for that gold medal, but it's a better medal than I got three years ago."
Kerr added: "It was fast, this crowd was absolutely electric. We went for it, we promised a fast and great race, and that was the result."
World Athletics president Sebastian Coe, who himself won two Olympic 1500m golds for Britain, had predicted that the final could be a "race for the ages" notably given the bitter rivalry between Ingebrigtsen and Kerr.
And so it proved, but not quite as Coe had foreseen as the unfancied Hocker stole the show with his late surge.
Kenya's Brian Komen briefly held the lead in front of a 69,000-capacity crowd at the Stade de France before Ingebrigtsen shot to the front of the pack at a cracking pace.
The field went through the opening 400 metres in 54.82sec, Kerr sat in third on Komen's shoulder and alongside Kenya's Timothy Cheriuyot, the 2019 world champion and silver medallist at the Tokyo Games three years ago.
Ingebrigtsen surged just after the 800m mark, but Cheruiyot kept with him.
At the bell for the last lap, the pack had split into single file.
Kerr made his move at 600m, tracking Ingebrigtsen and pulling close as they came into the home straight.
Kerr kicked, but suddenly Hocker appeared on the inside to deliver a super finishing surge for a fantastic Olympic victory that no one had predicted.
