Rudman set a combined time of a minute 56.3 seconds to win by almost a second from home athlete Anja Huber and American Noelle Pikus-Pace.
Her first run of 58.06s set the record. The overall champion tweeted afterwards: "Just won the Winterberg World cup and set a new track record by half a second!"
It was the 2006 Olympic silver medallist's first World Cup win of the season.
Lizzy Yarnold was fourth. She tweeted her congratulations to her team-mate: "Shelley was unbeatable today, great performance."
Yarnold has performed the better of the two so far this season, with silver at Park City then bronze in Whistler.
Latvian Dukurs won the men's event in 1:52.71 from Russia's Alexander Tretjyakov and German Christopher Grotheer.
Britons Kristan Bromley and Ed Smith were fourth and 12th respectively.