Two-time Wimbledon champion Petra Kvitova overcame a late wobble to set up a third-round encounter with fourth seed Paula Badosa.
The Czech had won 10 of the first 12 games and was leading 5-1 in the second set before Romania's Ana Bogdan won five games in a row.
Kvitova eventually stemmed the flow to take it to a tie-break, going on to win the match 6-1 7-6 (7-5).
Meanwhile, Spaniard Badosa beat Romania's Irina Bara 6-3 6-2.
Kvitova, 32, is one of just three former champions left in the women's singles draw along with 2019 champion Simona Halep and 2018 winner Angelique Kerber.
World number one Iga Swiatek, who is on a 36-match winning streak, is among the women in second-round action on Thursday, with the Pole facing Dutchwoman Lesley Pattinama Kerkhove on Court One (15:00 BST approximately).
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