The 15th seed, a semi-finalist at this year???s Australian Open, sent down seven aces as she completed a straightforward win over Brengle.
But 11th seed Karolina Pliskova suffered an early exit from the Rome tournament after slipping to defeat against the in-form Timea Bacsinszky.
The Swiss player ruthlessly completed a 6-4 6-0 win over Pliskova, taking her record to 26-5 this year.
Anastasia Pavlyuchenkova will face defending champion Serena Williams in the second round following a 6-4 7-5 win over Sam Stosur.
Ninth seed Angelique Kerber also advanced with a 6-2 6-3 win over Alize Cornet and was joined in the next stage by 13th seed Sara Erani, who defeated Daniela Hantuchova 6-4 7-6.