Muguruza defeated Ons Jabeur in a hard fought 3-6, 6-3, 7-6(4) win needing two hours and 23 minutes to do so.
It is another good run for the Spaniard who kicked off her season with a semi-final run at the Shenzhen Open after not reaching that point since claiming victory in Monterrey.
Mertens on the other hand eased through to the Quarter-Finals with a 6-1, 6-0 victory over Viktoria Kuzmova.
The champion in 2017 and 2018 in Tasmania, she has a perfect 14-0 record and this extends past the World No.61 who she also beat at the 2018 Australian Open by a similar scoreline.
There were also wins for the likes of Heather Watson, Elena Rybakina and Lauren Davis in what looks like a good Quarter-Finals in prospect in Hobart.
Veronika Kudermetova | 2 | 7 | 6 | ||||||
Catherine Cartan Bellis | 0 | 66 | 1 | ||||||
Lizette Cabrera | 2 | 4 | 6 | 6 | |||||
Kristyna Pliskova | 1 | 6 | 4 | 4 | |||||
Lauren Davis | 2 | 6 | 6 | ||||||
Magda Linette | 0 | 4 | 4 | ||||||
Garbine Muguruza | 2 | 3 | 6 | 7 | |||||
Ons Jabeur | 1 | 6 | 3 | 64 | |||||
Shuai Zhang | 2 | 4 | 6 | 6 | |||||
Kateryna Kozlova | 1 | 6 | 1 | 2 | |||||
Elena Rybakina | 2 | 7 | 6 | ||||||
Alize Cornet | 0 | 5 | 3 | ||||||
Heather Watson | 2 | 7 | 6 | ||||||
Fiona Ferro | 0 | 65 | 3 | ||||||
Elise Mertens | 2 | 6 | 6 | ||||||
Viktoria Kuzmova | 0 | 1 | 0 |