Top seed Karolina Pliskova lost her way in her first set at the US Open, but dominated the second after coming through a wobble.
Sofia Kenin was ousted in straight sets by Alize Cornet, who soared through to the last 16 of the WTA Premier tournament on Sunday.
An upset win over third seed Karolina Pliskova saw Ons Jabeur make more history in Doha on Wednesday.
Sofia Kenin's poor results continued on Tuesday, but Ash Barty had few problems reaching the last 16 in Doha.
Ons Jabeur pushed Simona Halep all the way, but the two-time grand slam champion was not to be denied a place in the last eight in Dubai.
More seeds were sent crashing in the Australian Open on Saturday as Karolina Pliskova and Elina Svitolina suffered straight-set defeats.
Saturday saw another Australian Open women's singles contender, Karolina Pliskova, fall in the third round.
It was a good day for the seeds at the Australian Open, where Simona Halep and Karolina Pliskova were among the winners.
Four women's singles seeds exited the Australian Open at the first hurdle, but Simona Halep and Karolina Pliskova did reach the next round.
We take a look at the best first-round matches at the Australian Open, including Venus Williams' meeting with Coco Gauff.