Langenhan timed 1 minute, 6.130 seconds in his second run to complete his second victory of the season in a combined time of 2:12.624.
David Moeller was second, trailing Langenhan by 0.122, as German lugers filled the top four places.
Johannes Ludwig was third and World Cup leader Felix Loch was fourth.
Loch, the Olympic champion, leads Moeller by 120 points with two events remaining in Latvia and Russia.
Langenhan's 100 points for the victory lifted him to third overall, trailing Loch by 183.