Ivanovic defeated seventh-seeded Dominika Cibulkova of Slovakia 6-2, 6-4. The third-seeded Serb, who won the event in 2008 and '10, was 3-0 down in the second set before reeling off four straight games.
The former top-ranked Ivanovic is yet to reach a final this season.
Earlier, Voegele won the last five games to complete her comeback against the 12th-ranked Stephens.
"To come back from 2-5 in the final set is incredible," said Voegele, who reached her third semifinal of the season. "I told myself to keep on fighting and I am proud that I was able to win."
Suarez Navarro beat fifth-seeded Kirsten Flipkens of Belgium 6-1, 6-3 to reach her fourth semifinal of the season and first on hardcourt. Suarez Navarro won the first eight points of the match and held serve throughout.