Spectacled Kazakh Shvedova broke Lisicki's serve in the third game before going on to record a 6-4 success in the opening set.
Former Wimbledon semi-finalist Lisicki, 22, came back into the match by taking her third break point in a marathon game at 4-3 and then serving out the second set 6-3.
The third was much tighter and at 3-2 to Shvedova was halted because of rain at SW19. After a lengthy break the match resumed and it was Shvedova who looked ready to take victory with a match point on the Lisicki serve at 5-4.
However, the German showed her resolve to save the match point and hold serve before breaking to-love in the next.
She faced a break-back point in the 12th game of the set but rallied to save it before completing the victory with an accurate lob.
Lisicki will play the winner of the Laura Robson-Maria Sharapova encounter on Centre Court in the last 16.