Neureuther was timed in 1:36.07 on his home slope and Benjamin Raich of Austria was third in 1:36.97.
Americans Bode Miller and Jimmy Cochran were among a group of skiers who failed to finish the first run.
Raich moved closer to overall World Cup leader Aksel Lund Svindal of Norway and stayed second in the slalom standings, ahead of Matt and behind Jens Byggmark of Sweden.
Matt, who won the slalom at the world championships in Sweden earlier this month, now has six slalom wins in his career. He also won a super-combi this season.
Neureuther also was second behind Matt after the first run at the world championships, but fell in the second heat.
This time, Neureuther handled the pressure in front of home fans on the Gudiberg hill where his father, Christian, was the last German to win a World Cup slalom in this resort 33 years ago.
Raich clocked the fastest second run to jump from seventh to third.