To deafening cheers from a packed Gangneung Ice Arena, the teenager speedster Choi raced the final two laps, holding off China in a frantic dash to the line as the Koreans successfully defended their Sochi title.
The Chinese were subsequently disqualified along with Canada, promoting Italy to silver.
Bronze went to the winners of the 'B' final, the Netherlands, who earned their place on the podium after setting a new world record of 4min 03.471sec.
Italian Arianna Fontana, winner of the individual 500m, was claiming a record seventh short-track medal.
"It feels great, I didn't really realise that until somebody told me after the race," said the 27-year-old.
For Choi it was a second gold of the Games, after her 1500m success at the weekend, to make up for her disqualification in last week's 500m.
The 19-year-old remains on track for a golden treble because she won her heat for the 1,000m to qualify for Thursday's quarter-finals.
Choi said: "It's my first Olympics, we tried our best to continue Korea's great record in the relay and of course it being in Korea we put lots of effort to do well at home."
It was South Korea's sixth Olympic relay title out of a possible eight, the only two to get away coming in Albertville in 1992, won by Canada, and China's triumph in Vancouver in 2010.
'Wasn't to be'
Earlier, the 12,000 crowd showed its sympathetic side in support of Christie, who lived up to her reputation as Britain's unluckiest Olympian.
The 27-year-old three-time world champion took second place in her 1,000m heat after a wipe-out, only to be hit with yet another disqualification.
Christie displayed real grit just to make the race after completing a remarkable return from injury following a weekend smash in the 1,500m semi-finals.
But she only made it a few metres in her qualifier when she went flying out after clipping the blades of Hungarian rival Andrea Keszler.
Sliding into the side padding she looked to be in pain, but to encouraging cheers from the crowd, Christie picked herself up, had her blades checked and lined up for the restart of the race.
Showing no ill effects she finished second to Dutch skater Lara van Ruijven.
But the judges dished out two yellow cards, demoting her to last of the four racers, with Pole Magdalena Warakomska inheriting her second place and with it qualification to the quarter-finals.
"It just wasn't meant to be," shrugged Christie.
She later told the BBC that if it hadn't been the Olympics, "I wouldn't have got on the ice" because of her injury.
Christie had worked miracles to make Tuesday's heat after being stretchered off the ice and taken to hospital for X-rays.
She also crashed in the women's 500m final in Pyeongchang.
And at the 2014 Sochi Games, she went home empty-handed after being penalised in all three of her events.