"This is the greatest day of my career. It is worth at least an Olympic gold medal," he said.
Tomba shared the lead with Swiss Urs Kaelin after the first leg but pushed himself to the limit in the second to clock a combined time of 2min 17.35sec. Kaelin was second in 2:17.80, 0.16sec better than the third- placed Christian Mayer of Austria.
Tomba, cheered on by Italian fans in this Dolomite resort, did a somersault and then kissed his dog after earning his 12th World Cup giant slalom win.
"It was wonderful to win here again, in front of my fans, my family and my dog," he said.
Tomba's win was made easier when Kaelin, who tied for the lead in the first leg on 1:09.17, lost precious time after slipping midway through the second leg.
Switzerland's Steve Locher, who won a World Cup giant slalom here last year, was third after the first leg but fell in the second. Mayer, fourth after the first leg, put on a fine show in the second, clocking the next fastest time behind Tomba.
Tomba, who now has 38 World Cup wins and who won here in 1987 and 1990, said he had felt confident of winning because of his form in finishing fourth in a giant slalom in the French resort of Tignes earlier this month."Tignes proved to me I could win this event. I was just waiting for it to happen," he said.
Tomba leads the overall World Cup standings with 550 points with Norway's Kjetil Andre Aamodt, who was fourth here, second on 302. Swiss Michael Von Gruenigen is third on 294.
Kaelin, whose sole World Cup victory was in the giant slalom in 1989, was happy just to have finished the second leg. "I wasted my chance to win when I nearly fell. So I have to be satisfied that I finished the leg, let alone finished in second place," he said.
Mayer, winner of last season's World Cup giant slalom title, has struggled this season but said his performance augured well for 1995. "I had a tough start to the season. The World Cup title in giant slalom put me under a lot of pressure from both fans and my team," Mayer said. "I've taken three weeks to find the right rhythm, but now I think I can start winning some races."
The race also saw the best performances of the season by veterans Marc Girardelli of Luxembourg and Paul Accola of Switzerland.
Girardelli, five-times overall winner of the World Cup title, was ninth after the first leg but had a blazing second run in which he was fourth fastest.
Accola, overall winner of the 1992 World Cup, leapfrogged from 16th place to 10th after a fine second leg.
Von Gruenigen, who dislocated his right shoulder on Wednesday, could return to the World Cup circuit next Thursday, weeks sooner than expected. He struck a pole in the second leg of an Alpine skiing World Cup slalom race in Lech, Austria. Doctors reset the shoulder and he was taken back to Switzerland for tests in Fribourg hospital.
Von Gruenigen won a giant slalom in Val d'Isere, France, last week after taking second place at Tignes.
A giant slalom is scheduled in the French resort of Meribel on December 29.