The German clocked a combined time of 2min 34.60sec to finish 0.10sec ahead of French racer Thomas Fanara, who had led after the first run.
In front of a massive crowd in unseasonably clement conditions, Austrian Marcel Hirscher claimed third, at 0.19sec.
It was Neureuther's first ever World Cup win in the discipline and the first by a German since 1973 in GS, in which is American Ted Ligety.
The American, however, failed to improve on his first run, when he finished third, catching a gate on his second run to send a ski shooting off.
"It's incredible, massive, crazy!" said Neureuther after his seventh World Cup career victory.
"I'd never have dreamed about winning a giant slalom."
Hirscher remains atop the giant slalom standings on 380 points from France's Alexis Pinturault (305) and Ligety (260).
The Austrian consolidated his second place in the overall World Cup standings on 575 points, with leader Aksel Lund Svindal (652) picking up a further 22 points with a 12th placed finish in the giant slalom.
Ligety was not too downhearted by his outing.
"I feel like I was starting to ski okay and find the rhythm of the course and then just crappy bad luck and just bounced into the gate and a little bit unexpectedly," the American said.
"That's just part of ski racing, but it's a kick in the groin, that's for sure."
Ligety added: "Felix is skiing well. He's one of my better friends on the World Cup tour and it's cool to see him get a win.
"That's not really a surprise. I think he's been pushing the envelope in GS for the last year and finally put together two good runs."