The Koreans fell behind after two minutes to a freak own goal from a throw-in, but drew level through Kim Un Hyang with 13 minutes of regular time remaining.
Jang Hyon-Sun netted the winner in the second period of extra time, seven minutes away from a penalty shoot-out.
North Korea now boast both age-group women's World Cup titles, having taken the under-20 version in Russia two years ago.
The pulsating and dramatic final between two powerhouses of women's football was a fitting way to end a tournament that captured the imagination of the New Zealand public, with a crowd of 16,162 pushing the tournament's total to 212,504, dwarfing the 52,630 that watched the 2006 under-20 women's World Cup in Russia.
The Koreans' horror start to the match made their win even more commendable, after they conceded a goal in unusual fashion from Cloee Colohan'ss long throw.
The Korean defence allowed the ball to bounce on the edge of their six-yard box, and keeper Hyong Myong-Hui was caught on her heels as it looped over her into the net.
Compounding Hyong's embarrassment was the faint touch she managed on the ball actually allowed the goal to stand, as goals cannot be scored direct from throw-ins.
Korea looked to hit back straight away but, despite mounting pressure, USA's defence held firm.
Both sides enjoyed patches of domination in the second half but just the Koreans appeared to be tiring and the Americans taking control, North Korea conjured a 77th minute equaliser.
A Ri Un-Ae thunderbolt rocked the cross bar from 35 yards, with fellow substitute Kim Un-Ju hooking the rebound back into traffic for Kim Un Hyang to nod over goalkeeper Taylor Vancil.
USA had the better chances in extra time but it was Korea who took their only real opportunity in the 113th minute, Ho Un-Byol unlocking the American defence for Jang to beat Vancil from just inside the area.
Speaking through an interpreter, Korean coach Ri Ui-Ham said he always confident his side could peg back the Americans after the early setback.
"Even when we went 1-0 down very early in the game, we showed strong character. We have been training very hard for a long time to achieve this, and we became stronger game by game," Ri said.
In the playoff for third, Germany broke a brave England with two goals in the final 20 minutes to run out 3-0 winners without really hitting full stride.
Two inch-perfect corners from Dzsenifer Marozsan were responsible for Germany's first two goals, the first picking out Inka Wesely for a back post header to open the scoring with 10 minutes gone.
Marozsan was the Golden Shoe winner with six goals for the tournament, and runner-up to Japan's Mana Iwabuchi as the tournament's best player.
She found Wesely again in the 74th minute but under closer attention, the defender this time side-footed the ball back across goal for Turid Knaak to score.
England captain Jordan Nobbs hit the cross bar shortly after, but Lynn Mester sealed the bronze medal with Germany's third goal two minutes from full time.
