Australian Dokic, who reach the last four at SW19 as a 17-year-old in 2000, beat Romina Oprandi 6-4 2-0 after the Italian retired hurt.
Seventh seed Vinci, also from Italy, was victorious 7-5 6-1 against fifth seed Dominika Cibulkova.
Earlier Slovak Cibulkova disposed of second seed Svetlana Kuznetsova 7-5 4-6 6-2 in the last eight.
Dokic made headlines in 1999 when she beat world No.1 Martina Hingis in the first round of Wimbledon, but later suffered personal problems.
She has enjoyed something of a comeback in recent years, reaching the quarter-finals of the Australian Open in 2009.
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