The FIS Alpine Skiing World Cup got underway in Solden with Austrian Fenninger beginning the defence of her overall and giant slalom titles in her own country.
And there was no shortage of drama for those in attendance as the top two could not be separated after both runs, resulting in a tie.
Shiffrin, the Winter Olympic and World Cup champion in slalom, led the way after the first run with a time of one minute and 17.93 seconds, with Fenninger just 0.09 secs adrift.
The second attempt proved just as close and both skiers clocked a combined time of two mins and 39.85 secs for a joint victory and 100 points each.
Victory marked Shiffrin's first in the giant slalom discipline, while Fenninger picks up her maiden triumph in Solden.
Commenting on a tricky course on the Rettenbach glacier, Shiffrin said: "I'm really psyched I made it down alive [in the second run]. This race was tough."
Eva-Maria Brem of Austria finished third ahead of compatriot Kathrin Zettel, while Italy's Federica Brignone rounded off the top five.
Frenchwoman Tessa Worley missed the majority of last campaign with an injured knee and produced a superb first run in which she placed third, but she did not fare as well on her second attempt and had to settle for seventh.