Eastbourne, East Sussex, UK, 22 June 2015 | AAP

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 hekd a third-set advantage before falling 7-6(4) 2-6 6-4 to New Zealand No.1 Marina Erakovic.

Tomljanovic went down 7-6(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) 6-3 7-6(4) to Angelique Kerber.

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