World number 72 Sania, who has never moved beyond the second round here, put up a clinical performance against the German, who enjoyed a career-best ranking of 57, a couple of weeks back but has now slumped to 73.
Sania, whose left leg was strapped just below the knee, completed the win with a backhand winner after an hour and 15 minutes on court number six.
Sania has not been able to cross the second round hurdle in the Grand Slams since 2009 and the fourth round appearance in the US Open in 2005 remains her best performance.
She will next face either 12th seed Polish Agnieszka Radwanska or Austria''s Patricia Mayr-Achleitner.
The clay court surface is not of the liking of Sania but the Indian looked quite comfortable against her opponent and played with a lot of confidence.
Sania played aggressively and thus committed a lot of unforced errors and also struggled with first serve but the overall game was so dominating that Kristina had no clue how to stop the Indian.