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.
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.
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 rivalry between Ingebrigtsen and Kerr.
And so it proved, but not qute as Coe had forseen 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 the Norwegian 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 kick for a fantastic Olympic victory that no-one, not least Coe, had predicted.
