Winner of the men's parallel event at home in Munich on New Year's Day, Neureuther skied a near-perfect second run to beat favourite and first leg winner Marcel Hirscher of Austria by 0.21 seconds.
Croatia's Ivica Kostelic, a four times winner of the slalom in the Swiss resort, was third and 0.25 behind Neureuther's winning combined time of one minute and 50.53 seconds. It was his 12th podium in Wengen.
The win was the fourth in the World Cup for 28-year-old Neureuther, the son of German slalom specialists Christian and Rosi Mittermaier.
Christian Neureuther won six World Cup slaloms in his career, including Wengen twice in 1973 and 1974.
"More than a dream, to win here was a goal," said Neureuther, who had already emulated his father in 2010 when he won his first World Cup slalom in Kitzbuehel.
"Classics like Wengen are special. I already found that out when I won in Kitzbuehel. But to be on the podium with Marcel, who looked unbeatable in the last three races, and Kostelic, who has won so many times here means a lot," he added.
Thanks to his second place, World Cup holder Hirscher increased his lead in the overall standings to 188 points over Norway's Aksel Lund Svindal.
The men's circuit moves to Kitzbuehel next weekend for a Super-G, a downhill, a slalom and a super-combined.
"To win one week before Kitzbuehel and two weeks before the world championships is obviously significant. But there's no rivalry between Marcel and I, we're great friends, often training together," said Neureuther.
"We're just trying to offer a great show," added the German, who trails the Austrian by 114 points in the slalom World Cup.
- Sports & Recreation