Safarova and Zakopalova each won points for the Czech Republic in singles matches Monday in the rain-delayed Fed Cup series in Spain. That allowed the Czechs to advance to the Fed Cup semifinals with a 3-2 decision over the Spanish.
They then hopped a jet to Doha where Safarova, behind a solid serving game, took out 16th-seeded Kirsten Flipkens 5-7, 6-4, 6-4; and Zakopalova sailed by Elina Svitolina 6-2, 6-4.
No. 9-seeded Ana Ivanovic advanced when Daniela Hantuchova retired with Ivanovic ahead 7-5, 1-0. Also out in a retirement was 10th-seeded Dominika Cibulkova, who was tied 5-5 with Alisa Kleybanova when play stopped. Cibulkova was beaten twice and Hantuchova once in Slovakia's 3-1 Fed Cup loss to Germany.
Samantha Stosur, the No. 12 seed, played Fed Cup matches last weekend in Australia but still was able to take a 6-4, 6-2 decision from Marina Erakovic.
Bethanie Mattek-Sands ousted 15th-seeded Eugenia Bouchard 7-5, 6-1 with five breaks in nine games receiving serve.
Other first-round winners Tuesday included Zhang Shuai, Stefanie Voegele, Monica Niculescu and qualifier Mirjana Lucic-Baroni.