Italian skier overcomes tricky snow and visibility conditions to triumph at the Stade Emile-Allais ahead of Sara Hector and first-run leader Petra Vlhova.
The 24-year-old looked the most comfortable of the top skiers in the conditions, registering a total time of 2:19.03 and backing up her victory in the GS season opener in Sölden.
Sweden's Sara Hector put in an outstanding second run to take second and claim her first World Cup podium since 2014.
Bidding for a fourth consecutive World Cup success, Petra Vlhova led after the first run but lost time on her Italian rival early on in her second descent and could only finish third overall.
Conditions clearly deteriorated as the day progressed with visibility particularly poor on the upper and middle sections of the course.
Double Olympic gold medallist Mikaela Shiffrin, who was third after the first run, got sideways midway through her second run and had to settle for fourth place.
With her third career World Cup win, Bassino extended her lead in the giant slalom standings and was delighted at retaining her series leader's red bib.
She told FIS afterwards, "After the first run, I thought to myself, 'I want to keep this red bib.' So I tried to push as hard as I could.
"In the first run, I skied so-so. I had nothing to lose so I tried to push and give my best. I'm really happy."
Bassino moves past Switzerland's Michelle Gisin into second in the overall World Cup standings with Vlhova still in front.
She will be hoping to make it a hat-trick of giant slalom wins as the field reassembles on the same hill tomorrow.