British women's number one Johanna Konta beat Madison Brengle 6-4 6-0 in 64 minutes.
Konta, seeded 25, won the last eight games to record her first victory in four attempts over the American.
She next faces Denisa Allertova after the Czech player shocked Australian Open champion - and semi-final conqueror of Konta in Melbourne - Angelique Kerber 7-5 7-5.
Konta, who won 24 of the 31 points contested in the second set and broke Brengle five times in the match, said: "Every single point we have played in the past has always been a battle, so I consider this a really good win."