With no British women remaining, the 12 qualifiers included Hungarian Czink, a seven-times veteran of Wimbledon who reached the third round last year.
The 29-year-old former world number 37 - now ranked 97 - beat Russia’s Marta Sirotkina 6-3 6-2 to enter the first-round proper in SW19.
Japan's Doi, however, will not be at Wimbledon after going down 4-6 6-4 6-4 to rising French starlet Kristina Mladenovic.
The 21-year-old reached the third round last year but lost out to the 19-year-old world number 161, who will make her Wimbledon debut.
Another Frenchwoman, Claire Feuerstein, will make her maiden appearance after she beat Maria Camerin of Italy 6-4 1-6 7-5.
A set of twins also qualified, as Czech sisters Karolina and Kristyna Pliskova beat Japan's Yurika Sema and France's Irena Pavlovic in straight sets.
Sesil Karatantcheva of Kazakhstan was beaten 6-3 4-6 6-4 by Sandra Zaniewska of Poland, while American Coco Vandeweghe broke late in the third to beat Laura Arruabarrena-Vecin of Spain 6-2 6-7 7-5.
In earlier results on Thursday, Serbian Vesna Dolonc beat Russian Valeria Savinykh, French Open junior champion Annika Beck of Germany beat Slovenian Petra Rampre,while Slovakian Jana Cepelova defeated Ekaterina Bychkova of Russia, all in straight sets.
Three rounds of men and women's qualifiers took place for Wimbledon, with a combination of players ranked in and around the top 100 and local wildcards making up the draw.
No Britons progressed from either route, although most top local players were granted automatic entry into the first-round proper either by right or through wildcards.
Women’s singles qualifiers:
Coco Vandeweghe (United States)
Kristina Mladenovic (France)
Claire Feuerstein (France)
Sandra Zaniewska (Poland)
Vesna Dolonc (Serbia)
Annika Beck (Germany)
Melinda Czink (Hungary)
Jana Cepelova (Slovakia)
Kristyna Pliskova (Czech Republic)
Mirjana Lucic (Croatia)
Camila Giorgi (Italy)
Karolina Pliskova (Czech Republic)
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