Draper will face Tommy Paul or Christopher O'Connell on WednesdayBriton Jack Draper reached the last 16 of the Adelaide International 2 but compatriot Dan Evans was knocked out in straight sets.
Draper eased past Italian Lorenzo Sonego 6-4 6-2, while fifth seed Evans lost 5-7 5-7 to unseeded American Mackenzie McDonald.
Briton Kyle Edmund faces Serb Miomir Kecmanovic later on Monday.
In the women's event, 2022 Australian Open finalist Danielle Collins beat Karolina Pliskova 6-2 6-4.
And in a battle between current and former Wimbledon champions, Kazakhstan's 2022 winner Elena Rybakina lost 6-3 7-5 to Czech Petra Kvitova.
There are two ATP-WTA Adelaide Internationals this month as players gear up for next week's Australian Open, with Novak Djokovic and Aryna Sabalenka winning the titles in week one.
Draper, who will compete at the Australian Open for the first time, will face American eighth seed Tommy Paul or Australian lucky loser Christopher O'Connell in the next round.
The top four seeds - Andrey Rublev, Pablo Carreno Busta, Karen Khachanov and Roberto Bautista Agut - were given byes into the last 16.
In the women's draw, American Collins continued her fine form and cemented her status as one of the favourites for the Australian Open singles crown with a straight-set win over former world number one Pliskova.
Collins will face Jil Teichmann in the next round after the Swiss qualifier defeated 2021 French Open finalist Anastasia Pavlyuchenkova 7-5 6-4.
It was the Russian's first match for eight months after sustaining a knee injury last summer.
World number one Iga Swiatek and third-ranked Jessica Pegula had been due to play this week, but both pulled out after their exploits at the United Cup with Poland and the United States respectively.
