In a closely contested match, Bartunkova broke serve up 5-4 in each set to come away with the upset. Linda Fruhvirtova also won in her home country Monday, beating Germany's Mona Barthel 7-6 (4), 6-4.
Her older sister, Brenda Fruhvirtova, was not so lucky, falling 6-1, 6-1 to French qualifier Fiona Ferro. Another Czech competitor, Anna Siskova, also lost her opening-round match, 6-4, 6-4, to Germany's Tamara Korpatsch. American Alycia Parks defeated Austria's Julia Grabher 7-6 (3), 6-2.
Transylvania Open
Top-seeded Emma Raducanu started her tournament with a 6-0, 6-4 victory over Belgium's Greet Minnen on the indoor hard courts in Cluj-Napoca, Romania.
The British competitor needed only 70 minutes to advance, facing no break points while converting four of the seven break opportunities she created.
No. 3 seed Solana Cirstea also began her run in the home-country tournament with a straight-sets win, 6-4, 6-4, over Kamilla Rakhimova of Uzbekistan.
In the only three-set match of the day, Russia's Anastasia Zakharova came back to beat wild-card competitor Karolina Pliskova of the Czech Republic, 4-6, 6-2, 6-2. Another Romanian, Ana Bogdan, was defeated in straight sets by Poland's Maja Chwalinska, 6-3, 6-2.
Abu Dhabi Open
Lucky-loser Aliaksandra Sasnovich of Belarus pulled off a 6-4, 3-6, 6-1 upset of eighth-seeded Spaniard Paula Badosa in opening-round action on the outdoor hard courts in the United Arab Emirates.
That was hardly the only drama of the day, as No. 7 seed Jelena Ostapenko from Latvia saved a pair of match points and survived being broken six times in a 5-7, 7-6 (4), 6-2 win over Oksana Selekhmeteva of Russia in one of four three-set matches.
Indonesia's Janice Tjen defeated Australia's Maya Joint 7-6 (6), 3-6, 6-3, and Simona Waltert of Switzerland outlasted Australia's Daria Kasatkina 7-6 (5), 3-6, 6-4.