American Mikaela Shiffrin, who had won on the Vermont slope on all five occasions she has competed, finished in fifth place 0.59 seconds behind the tied pair - both first time World Cup winners in slalom.
It was the first tie in a women's race since Flachau in 2011, when Maria Riesch Hoefl of Germany tied with Tanja Poutiainen in slalom.
The course began to break up during the second run leading to some slow times for many of the contenders with later runners at a clear disadvantage.
Austria's Katharina Truppe was third, 0.22 seconds off the winning pace while Olympic slalom champion Petra Vlhova of Slovakia was fourth.
Holdener, who won bronze in slalom at the Beijing Winter Olympics, had never won a World Cup slalom while it was Swenn-Larsson's first ever victory on the circuit.
Holdener had finished on the podium in slalom on 30 occasions before Sunday's race and was delighted to have finally clinched top spot.
“It does taste sweet, but in an hour or two it will be even more crazy,” said Holdener.
“I was thinking maybe we have a chance, because it's not that easy to ski, it's a little bit bumpy. I fought really hard for this one," she said.
Swenn-Larsson could not hide her joy. “I am so happy. I have a lot of emotions, it is a dream come true,” she said.
“I fought really hard for this one, I’ve been fighting for it my whole life.
“I am proud. To beat Mikaela – I didn’t do it many times in my life. She is an inspiration, she is the best skier, so it feels amazing," she said.
Shiffrin put herself in prime position for victory after posting the fastest time in the first run - finishing 0.21 seconds ahead of Holdener.
But with the course deteriorating, Franziska Gritsch of Austria, who was 30th in the first run and first out in the second leg, watched as 20 skiers could not better her time.
Racer after racer found they could not maintain momentum in the flats in the lower sections while the Austrian watched on almost in disbelief.
Gritsch, who posted the fastest time on the second run, finished eighth while her Austrian team-mate Katharina Liensberger, third after the first leg, skied out early into her run.
It was an indication of how difficult the course had become that Shiffrin's second run was 2.86 seconds slower than her first effort.
Shiffrin who won both the opening slalom events at Levi, Finland last week refused to blame conditions.
"Wendy and Anna finally got their first win and it is tied - it is a pretty special day actually," said the American.
"It felt like the conditions were OK but some spots I gave maybe a little bit of respect because of the tracks but it was quite good and no different for me than it was for Wendy, Swenn-Larsson or Petra," she said.
