Vien came in first in the women's 200m individual medley category, with a time of 2min 12.66sec, setting a new record for the Games.
The old record of 2:14.53 was set by Kaitlyn Jones of the US four year ago in Singapore.
Siobhan BernadHaughey of Hong Kong took the silver, just 0.55sec behind, and Meghan Small of the US won the bronze medal.
Vien, 17, earlier finished second (2:16.02) in the fourth heat of the qualifying round, then booked her place in the final, which saw her ranked sixth among the eight best athletes.
However, the Vietnamese surprised all with a strong splash in the final, creating a larger distance from her rivals after every 50m-lap.
Vien also made national history as the first-ever swimmer winning at the Youth Olympics, setting a new national and Southeast Asian Games' record.
"I am so happy. I just swam, swam, swam and I won. That's all," Vien was quoted as saying on nanjing2014.org.
Haughey added, "All I wanted to do was beat my personal best of 2:13.35, and I did, and I won a medal at the same time. My worst is the breaststroke, so I worked hard at it and just kept going."
Small, who went into the final with the best heats time, noted, "There was some pressure and I've had a stomach bug the last few days. Also, the breaststroke slowed me, but I'm happy with what I got."
In the upcoming days, Vien will compete in eight other events, among them the 400m and 800m freestyle, which are her strongest events.
The Vietnam team also pocketed one silver medal in the men's 56kg category in weightlifting.
Nguyen Tran Anh Tuan failed to defend Vietnam's gold medal won in the last Games.
He suffered a stretched ligament prior to the competition, causing his poor performance of 243kg. This placed him in second position, behind Chinese Meng Cheng, who lifted 283kg.
AdkhamjonErgashev of Uzbekistan came in third with a 243kg result.
With one gold and one silver from the first day of competition, Vietnam has successfully reached its target.
The second Youth Olympics opened in wet Nanjing on Saturday with International Olympic Committee president Thomas Bach encouraging the teenage athletes to have fun and embrace social media.
"You are here to enjoy the competitions and to deliver your personal best performance," Bach said.
"You are here to experience and promote the Olympic values of excellence, respect and friendship. You are here to celebrate the Olympic spirit."
Chinese President Xi Jinping declared the 13-day Games, for 3,800 athletes from 204 countries competing in 28 sports, open in front of 60,000 fans in Nanjing Olympic Sports Centre Stadium.
United Nations Secretary General Ban Ki-moon was also present for the lights, music and dancing, fireworks and cultural ceremony, which ended with Olympic diving champion Chen Ruolin lighting the Olympic cauldron.
Australia's Brittany Dutton won the first gold medal, winning the women's triathlon at the Xuanwu Lake Triathlon Venue in 59min 56sec.