The pair edged out Swiss team Patrizia Kummer and Dario Caviezel in the Big Final, while Germanany's Selina Joerg and Stefan Baumeister narrowly beat their Russian counterparts in the Small Final.
The result means Karl and Ulbing haven now won three mixed parallel slalom titles in a row, having taking the crown in Bad Gastein and Moscow in January.
Despite this, Austria sit third in the Overall Nation Cup, comfortably behind leaders Switzerland. "It's just amazing. A triple victory in all team events. This girl always did a great job and always gives me a little advantage," a delighted Karl said.
"There's a real satisafaction after some missed races the last time."