January 18, 2017 0808 GMT
The 25-year-old broke the world number 25 in the opening game and dropped only four points on serve in the first set, BBC reported.
The world number 10 wasted four match points on her own serve in the eighth game of the second set, but broke Gavrilova in the ninth to seal victory.
Konta will play Russian world number 26 Daria Kasatkina in the quarterfinals.
The 19-year-old beat world number one Angelique Kerber earlier. Third seed Dominika Cibulkova and fifth seed Svetlana Kuznetsova were also beaten on Tuesday.
Konta said, "It's such a strong tournament, such depth. I know going into every single match that it's going to be a tough one and I'm just going to have to, first and foremost, take care of things my end."