The 26-year-old, who was born in Coni 80 kilometres from Sestriere, was second after the first run but put in a solid second leg to complete in a combined time of 2min 28.89, finishing 0.11 seconds ahead of the Swede Sara Hector.
Bassino's 1min 12.37sec placed her behind Vlhova on the first run but the Slovak was unable to maintain her pace and had to settle for third, 0.40sec adrift.
It is the sixth World Cup win of Bassino's career, all of them coming in the giant slalom.
"To win at home, in front of an unbelievable Italian public, is super," said Bassino.
"It was a real battle, the course was very complicated, I tried to give my maximum.
"It is really a dream I have fulfilled."
Olympic slalom champion Vlhova is still seeking her first win of the campaign, her two third placed finishes in the slaloms in Levi, Finland, her best showings so far.
US ski great Mikaela Shiffrin - Olympic champion in the giant slalom in 2018 - was fourth quickest after the first run but fell away to come in sixth, 1.96sec behind Bassino.
Another Italian Federica Brignone, victorious on this track two years ago, set the fastest time before being eclipsed by Hector who shaved 0.55sec off it.
Brignone missed out on the podium, finishing fourth ahead of French skier Tessa Worley - the World Cup holder in the discipline - and Shiffrin.
The American won both of the slalom races in Levi and will be seeking to add a third victory in the discipline on Sunday.
