Casey Dellacqua is the first Australian through to the second round of the Wimbledon warm-up event at Eastbourne.

Dellacqua cruised past Slovakian Anna Karolina Schmiedlova 6-2 6-4 on Sunday, as Jarmila Gajdosova joined her in the main draw with a 6-4 6-1 final-round qualifying win over German Tatjana Maria.

But qualifying defeats for Daria Gavrilova and Ajla Tomljanovic left the rising youngsters heading for the practice courts to fine-tune their grasscourt games before the season’s third grand slam gets underway in London on Monday week.

Fresh off a 6-0 6-1 humbling of returning British ace Laura Robson, Gavrilova was unable to live up to her top seeding as she blew a handy third-set advantage in a 7-6 (7-4) 2-6 6-4 loss to New Zealand No.1 Marina Erakovic.

Tomljanovic went down 7-6 (7-5) 6-3 to American Irina Falconi.

Dellacqua’s reward for her straight-sets victory is a second-round clash on Tuesday with eighth seed Karolina Pliskova, the Czech who lost Sunday’s cliffhanger final in Birmingham 6-7 (5-7) 6-3 7-6 (7-4) to Angelique Kerber.

In other first-round matches, American Sloane Stephens beat Brit Naomi Broady 3-6 6-3 7-6 (7-4), Swiss Belinda Bencic defeated German Mona Barthel 6-4 7-6 (9-7) and France’s Caroline Garcia eliminated Italian Roberta Vinci 6-2 6-2.

Alison Riske of the USA upset Frenchwoman Alize Cornet 6-0 6-3, American CoCo Vandeweghe ousted Swede Johanna Larsson 6-7 (3-7) 6-1 6-1 and local qualifier Johanna Konta took out Kazakhstan’s Zarina Diyas 6-3 6-2.

Gajdosova faces American qualifier Lauren Davis in her first-round match on Monday, while Australian No.1 Samantha Stosur, as 16th seed, enjoys a bye and opens her title quest on Tuesday against Erakovic or Bulgarian Tsvetana Pironkova.