Ashleigh Barty has dispensed with France's Kristina Mladenovic in straights sets, the Australian advancing to the third round at Britain's Eastbourne International.
However the news wasn't so good on Tuesday for compatriot Daria Gavrilova, the 15th seed falling to Poland's Agnieszka Radwanska 5-7 7-6 (4) 6-0.
Barty came away with the 6-3 6-2 win in 76 minutes and on the strength of a superior first serve although the match only featured six aces, four of them the Queenslander's.
Both women registered five double faults in stark contrast to Gavrilova's capitulation, in which she failed on both serves 17 times against Radwanska.
Petra Kvitova meanwhile sent Kateryna Bondarenko packing in straight sets to advance.
The third seed, who won her fifth title of the season on Sunday in Birmingham, triumphed 7-5 6-3 and looks in impervious form ahead of her bid for a third Wimbledon title.
Her career looked seriously in doubt 18 months ago after a knife attack which led to surgery on her playing hand.
"I'm pretty happy with my win today," Kvitova said.
"Obviously I'm a little bit tired but I got a hit this morning before the match, a warmup.
"The whole tournament (in Birmingham) was more relaxed for me from my side. It was great that I hopefully will save some energy for the next weeks. I felt good with the body, so that's important."
In a tight first set, Kvitova secured the first break but Bondarenko broke back when the Czech was serving for the set.
However Kvitova broke straight back and held serve to love, clinching the first set with a delightful serve and volley.
Bondarenko went 3-1 up with a break in the second as Kivitova double-faulted.
But it was the last game the Ukrainian won.
British No. 1 Johanna Konta will face top-seeded Caroline Wozniacki after easing past Serbia's Aleksandra Krunic 6-1 6-3.
The 13th seed stuttered at times and perhaps benefited from Krunic injuring herself while sliding into the net toward the end of the first set.
Earlier, Aryna Sabalenka of Belarus upset sixth-seeded Julia Goerges 1-6 6-4 6-4, while American Danielle Collins beat 16th-seeded Carla Suarez Navarro of Spain 6-2 6-4.
Collins will next face Angelique Kerber after the German comfortably defeated Dominika Cibulkova 6-3 6-3.
Fifth-seeded Jelena Ostapenko of Estonia dismissed Kaia Kanepi 6-3 7-5.
In the men's draw, fifth-seeded Leonardo Mayer beat Gilles Simon 6-4 7-6 (4) in the first round.
Seventh-seeded Steve Johnson is also safely through after easing past Daniil Medvedev 6-2 6-4.
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