After eliminating world No.1 and defending champion Naomi Osaka, the 13th-seeded Bencic lost just six points on her first serve in a tight two-setter against first-time Grand Slam quarterfinalist and good friend Vekic for a 7-6(5) 6-3 win in one hour and 40 minutes.
It was the 23rd-seeded Vekic who first led by a break in the opening set, but Bencic recovered immediately and edged out the set on the fourth set point.
The second set went with serve until the seventh game when Bencic broke at love for a 4-3 lead.