Second seed Varvara Lepchenko went safely through to the second round of the inaugural Bol Open after defeating Croatian wildcard Ana Vrljic 6-1 7-5 in straight sets.
Lepchenko converted all five of her break-point chances on the way to a comfortable win.
Fellow American Anna Tatishvili came through a match lasting two hours and 40 minutes against Paula Kania to advance 6-4 6-7 (4/7) 7-5.
Her countrywomen Sachia Vickery and Jennifer Brady enjoyed more straightforward routes to the second round with straight-sets wins.
Vickery won 6-2 7-5 against Croatian wildcard Tena Lukas, while Brady upset number eight seed Patricia Maria Tig 6-2 6-1.
Elsewhere, Ipek Soylu survived a second-set fightback from Julia Glushko to advance 6-3 0-6 6-1, Stefanie Voegele defeated Andreea Mitu 6-3 6-2, Ivana Jorovic overcame qualifier Isabella Shiniakova 7-5 6-2 and Elitza Kostova beat fellow qualifier Ekaterina Alexandrova 6-1 7-6 (7/4).
Source: PA