Zvonareva, who was last year's runner-up to Kim Clijsters, fired 16 winners and beat the 25th-seeded Lisicki 6-2, 6-3.
After watching her opponent make 28 unforced errors, Zvonareva moved on to face No. 9 seed Samantha Stosur of Australia, who shook off losing a long second set tiebreaker to beat 25th-seeded Russian Maria Kirilenko on Sunday.
Stosur fired 38 winners to Kirilenko's 23 and settled in for a 6-2, 6-7 (15-17), 6-3 victory. She was also a quarterfinalist at last year's U.S. Open.
The 26th-seeded Pennetta battled past No. 13 Peng Shuai of China 6-4, 7-6 (8-6), overcoming a 5-0 deficit in the tiebreaker.
Pennetta swatted nine aces and broke her opponent's serve six times en route to reaching the quarterfinals at the year's final Grand Slam for the third time in her career (2008-09).
The 29-year-old Pennetta will next face Kerber, who handled Romanian Monica Niculescu 6-4, 6-3.