The win is Dressen's second downhill success of the season, after taking the first World Cup event in Lake Louise.
The German finished a comfortable 0.16 seconds ahead of Aleksander Aamodt Kilde of Norway, who edged Frenchman Johan Clarey into third by a hundredth of a second.
In-form Pellegrino kicks off New Year with sprint success
The event ended with 2016 and 2017 champion Peter Fill being applauded by all competitors and dowsed in champagne by his Italian countrymen, after finishing in 31st place, in the last of his 355 World Cup starts.
Kilde completes Val Gardena double with Downhill victory
Petra Vlhova leads the way after first run