Joining eighth seed Boulter were Xu Mingge, Sonay Kartal, and Francesca Jones, though Boulter and Kartal are set to face each other in the next round.
"I've played enough of them now. It's just another match for me. I have so much respect for Sonay, she's an incredible tennis player," said Boulter after the win over Sun.
"I've always said to her that she's going to pass my ranking. I know how good she can be and dangerous.
"We actually played a really close match on grass quite a few years ago, so I know it's going to be an absolute battle."
Boulter, currently on an 11-match winning streak at her home tournament, is aiming to become the first player in Nottingham Open history to claim three consecutive titles.
The 17-year-old Xu beat American Katie Volynets 6-3, 6-3, setting up a clash with Polish sixth seed Magda Linette, who overcame Filipino Alexandra Eala 6-4, 6-3.
Jones defeated compatriot Harriet Dart 7-5, 6-4 and will now face Czech seventh seed Linda Noskova.
Slovakia's Rebecca Sramkova battled past Germany's Laura Siegemund 7-6(2), 4-6, 7-6(6) and is set to meet fourth seed Yulia Putintseva.
Haddad Maia knocked out by Kessler
Late in the day, top seed Beatriz Haddad Maia was stunned by American McCartney Kessler, losing 7-5, 6-7, 7-5 in an epic that lasted almost three hours.
Kessler will take on China's Zhu Lin, while Canadian fifth seed Leylah Fernandez will play Spain's Cristina Bucsa, who defeated Yuliia Starodubtseva 6-3, 6-3.