Dagar, one of the four Indians playing in the event, shot two-over 74 on a difficult scoring day, with only two players in the 126-player field producing sub-par rounds at the Westlake Golf Club.
The afternoon saw winds, which gusted over 50 kilometres per hour at times.
Millie Saroha, making her start outside India this year, shot 77 and was just inside the expected cut line. Astha Madan (81) and Tvesa Malik (81) are the other Indians in the field.
Boqvist and Schober will head into the second round of the Sunshine Ladies Tour and Ladies European Tour co-sanctioned event with a slender one shot advantage over three-time champion Lee-Anne Pace from South Africa, Spain's Silvia Banon and Sweden's Julia Engstrom.
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