The 22-year-old fourth seed from Perth needed only 72 minutes to triumph 6-2 6-1 and set up a meeting with American Ashlyn Krueger, a 6-3 6-1 winner over Lanlana Tararudee of Thailand.
Gibson arrived in Japan off the back of disappointing opening-round defeats in Beijing and Wuhan.
But after overcoming Brit Harriet Dart 7-5 7-6 (8-6) in the first round, the world No.42 was in a more menacing mood on Wednesday against her Austrian opponent.
Kraus, 24, was broken in her opening service game and again to bring the first set to an end.
The world No.76 fared no better in the second, only taking Gibson to deuce on serve once in the contest.
Better news for another Austrian in Lilli Tagger, who recorded a second-round straight-sets win.
The conqueror of fifth seed Liudmila Samsonova in round one, 18-year-old Tagger was victorious 7-5 6-3 over Czech teen Tereza Valentova and will next face Katie Boulter.
Alex de Minaur's English wife, the current world No.58, was another comfortable winner in the final match of the day, 6-2 6-1 over Swiss veteran Viktorija Golubic.
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