A first career World Cup victory for Gross denied first-run leader Fritz Dopfer of Germany his first win by 0.02.
Overall World Cup leader Marcel Hirscher of Austria extended his standings lead in third, a further 0.01 behind Gross's combined two-run time of 1 minute, 56.70 seconds.
At age 28, Gross finally won after three podium finishes in the 2012 season, and a fourth place in the Sochi Olympics slalom last February where he tied with Dopfer just 0.05 off the bronze medal.
"I am very, very happy," said Gross, who has overcome back injuries. "I have worked really hard this summer and this season to reach this result."
On a good day for the Italian slalom team, 2010 Olympic champion Guiliano Razzoli placed fourth, 0.55 behind his teammate, equaling his best result in more than three years.
Another Italian, 36-year-old Patrick Thaler, was second fastest in the first run but skied out in the afternoon when poised to extend his own World Cup record as the oldest man to finish on a slalom podium.
Hirscher now tops the season-long slalom standings after previous leader Felix Neureuther of Germany failed to finish the first run.
Earning 60 World Cup points, Hirscher leads Neureuther by 56 in a repeat of their duel last season which the Austrian edged on the final day.
The three-time defending overall champion also tops those standings by 212 from Kjetil Jansrud of Norway who skips slalom events.
Hirscher said it was "a perfect weekend with 160 points" after winning the classic giant slalom Saturday, and praised Gross and the surging Italians.
"He's a very nice guy, he's good looking," Hirscher quipped, "and a very good skier. I think the Italians are getting in shape for the world championships."
Dopfer used his No. 1 start bib to be fastest in the morning through steady snowfall and on a tricky race surface.
With victory in sight on a clear afternoon, he let a half-second lead slip on the steep final slope and added to a resume of near misses, including five runner-up finishes in World Cup races.
"I'm pretty satisfied and confident with my second place," the 27-year-old German said. "I tried everything and pushed really hard."
Still, Dopfer's consistent season with top-10 finishes in each of his nine races lifted him to third overall, though trailing Hirscher by a distant 330 points.
Ted Ligety of the United States is seventh overall after placing 22nd Sunday, 2.02 back.
David Chodounsky was the best-placed American in 11th, trailing Gross by 0.96.
A 19th place Sunday for Luca Aerni proved the best Switzerland could manage in a signature Alpine meeting for the host nation this weekend, which last won at Adelboden in 2008.
The World Cup moves to nearby Wengen where four different Swiss racers have won the classic Lauberhorn downhill in the past six years.