Shiffrin, 18 years and 345 days old but already a world champion last year, skied fast and clean through the first leg but almost blew it on the second when she ripped down the top part of the course and made a big error at the midpoint.
The Vail-born skier's outside ski lifted into the air as she fought for balance before regaining control and finishing 0.53 clear of Austrian silver medallist Marlies Schild.
"I felt like I was really charging out of the start and had good speed," the bubbly Schiffrin, also the youngest U.S. Alpine skier to medal at a Games, told reporters after the happy ending.
"All of a sudden I was like 'Oh, I'm going out of the course'. It was a pretty terrifying experience really. I mean, it's probably not the worst thing that could happen in my life but in that moment I was pretty pissed at myself."
Her mother Eileen, watching at the finish, might have felt more like calling an ambulance.
"I really almost had a heart attack, but thank God Mikaela was so quick to regroup and get going again, because then I could calm down. But I'm pretty sure I almost had to be defibrillated," she told reporters.
Shiffrin's team coach Roland Pfeifer described the moment as 'brutal'.
"Sometimes Mikaela, for some reason when she's really hammering it, gets a little in the back seat," he said. "She's overdoing it, she skis a little bit too hard, shooting out all of a sudden.
"I can't describe how I felt. I thought 'It's over'. But luckily she was really ripping the top of it (the piste) and it was just good enough to win."
Schild, the oldest slalom medallist at 32, took her fourth career Olympic medal - three silvers and a bronze - with compatriot Kathrin Zettel tearfully celebrating her first with third place.
"Of course a gold medal would have been a dream but the dream died in the first run," said Schild, who had been only sixth fastest at that point, after equalling the Austrian record of four medals.
"I did not lose the gold, I won the silver in the second run."
Germany's Maria Hoefl-Riesch, the 2010 champion bidding to become the first woman to win back-to-back slalom titles in her final Games, finished fourth after being in second place at the end of the first run.
Slovenia's Tina Maze, chasing her third gold medal of the Games after her success in downhill and giant slalom, slipped from a medal position to eighth.
Schild's medal was a bittersweet success with sister Bernadette, fourth after the first run, hooking a gate on the second trip down the slope and went out.
"It was really bad for her today that she could not finish the second run, but I think she will have much more chances to make medals," she said.
"Of course I'm really happy for my sister," said the younger Schild. "But I knew she had nothing to lose after her first run and if what she planned to do worked out she would be super-fast."
If Shiffrin's second leg was ragged, the first was controlled and confident.
"She skied perfectly like she always does," Bernadette Schild had said of a woman who has replaced the absent Lindsey Vonn as the smiling face of U.S. women's skiing. "She makes no mistakes, that's what makes her so fast."
Italy's Paoletta Magoni was the previous youngest Olympic slalom champion, winning gold in Sarajevo in 1984 at the age of 19 years and 156 days. Switzerland's Michela Figini won the downhill that same year at the age of 17.
The gold was the second in Alpine skiing at the Sochi Games for the U.S. team after Ted Ligety's giant slalom win on Wednesday.