Grubben crossed the line in a winning time of 46 minutes and 24.3 seconds, with Baverel-Robert - also perfect on the day - finishing a futher 1:06.5 back.
Martina Glagow overcame one miss on her first shoot to claim the bronze medal in front of Norway's Tora Berger.
Swedish World Cup leader Anna Carin Olofsson would have won the title had she shot clear on her final five tries at the range, but missed two at the last standing shoot for a total of four misses on the day.
Antholz-Anterselva
Grubben goes out on top
14/02/2007 AT 14:59
Despite the catastrophic shooting performance, Olofsson finished in fifth just under two minutes behind Grubben thanks to the day's fastest ski time.
Defending champion Andrea Henkel was the second-best German in sixth-place.
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Antholz-Anterselva
Greis upsets Bjoerndalen
11/02/2007 AT 15:01
Antholz-Anterselva
Henkel leads German sweep
10/02/2007 AT 14:08