Bassino sealed a first career win by retaining her first-run lead to edge Federica Brignone by 0.26 seconds. Brignone, who won this race last year, was first to greet her teammate and hugged her in the finish area.
Shiffrin was a further 0.03 back in third for a fourth straight top-five finish in GS at the Vermont venue without taking the win.Still, the three-time defending overall World Cup champion extended her standings lead with a third podium finish to start the season.
Shiffrin was also favoured to claim a slalom win for the fourth straight year on the Super Star course overnight.
Bassino is a former junior world champion in giant slalom, who had four previous third-place finishes on the World Cup circuit. She also placed fifth at the 2018 Pyeongchang Olympics, where Shiffrin won and Brignone took bronze.
"I finally put together two runs," Bassino said. "I tried to focus just on myself and to ski like I know how. Then I saw the green light and I thought, 'Wow."'
Bassino clocked under 50 seconds in bright sunshine for each run which was shortened due to gusting winds at the scheduled start higher up the mountain.
Kiwi Piera Hudson placed 44th on run one but in World Cup races only the 30 fastest racers from the first run of two qualify.
Hudson will be looking to back up the career best result she recorded at last year's Killington Cup, becoming the first NZ racer in 15 years to achieve a top 30 result.