Pranjala and her seventh seed Chinese partner Wushuang Zheng cruised past the unseeded pairing of Anastasia Gasanova and Maia Lumsden 7-5 6-4.
Earlier, the 17-year-old Nagal lost 6-2 3-6 4-6 to eighth seed Korean Yunseong Chung in second round.
Pranjala though had exited from the girls singles after losing her first round contest.