The American, who led after the first run, overcame a tricky course set by her rival Petra Vlhova's coaching staff to beat Italy's Federica Brignone by 0.82 seconds, with a total time of 2:19.63 – her 67th career World Cup win and first in giant slalom since December last year.
Shiffrin had a lead of 0.07 seconds over Marta Bassino and 0.14 seconds over Brignone after the first leg, but Bassino slid off course in the second run.
It was Bassino's first giant slalom defeat of the season, with the red bib wearer having won during the season-opening weekend in Sölden as well as on Saturday in Courchevel. Brignone takes over as the new giant slalom standings leader.
France's Tessa Worley, part of the new Olympic Channel original series Cirque Blanc launching this week, finished third.
In sunny weather conditions, Shiffrin skied the perfect race to increase her gap over Brignone and clinch her first win of the season and her first triumph since the death of her father in February.
Shiffrin collapsed to her knees crying with emotion during the post-race presentation as her name was announced as the winner.
Slovakia's Vlhova, who leads the overall Crystal Globe World Cup standings, slid out of the race in the last segment of the first run for her first did-not-finish of the season.
Speaking to FIS through tears after the race, Shiffrin said: "It's pretty hard to explain, because really 95 per cent of me felt that I couldn't do it, but just a small bit of me at the right time… it's crazy to be back here."