Sanders, Tomljanovic lead Australia into BJK Cup semis
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In Friday's semi-final, Russia will take on the United States and Australia will face either the Czech Republic or Switzerland who are playing the last Group D game later on Thursday.
Sanders made it very clear that she would set the rhythm from the start, subjecting Hatouka to a mix of fierce groundstrokes and vicious drop shots.
Leaning on a solid serve throughout the match, Sanders cruised to a win in just over an hour without offering the big-serving, big-hitting Belarusian youngster a single break point.
"I played good tennis today, I was very nervous but happy to get the win," said Sanders.
"I was trying to compete as hard as I could and hopefully get a few opportunities which I did."
"I served really well, I didn't get broken the whole match so I'm really happy with how I served today."
Tomljanovic got off to a stumbling start after she had sat out Tuesday's tie in which Australia had beaten Belgium 2-1 in the Group B opener.
Sasnovich won four games in a row, and even though Tomljanovic put up some resistance, she took the first set.
Tomljanovic failed to break her in the 10-minute game two of the second set, but she managed two breaks a moment later and took the second set as Sasnovich double-faulted on the set point.
The lost set meant that Belarus were out of contention with Belgium still waiting for the final score.
Though increasingly nervous, Sasnovich did not give up and earned three breaks in the final set, but she gave away four and finally crumbled, failing to return a serve on the match point.
"There's really no greater feeling, I was happy I could come out today and the fact that I got the point makes me unbelievably happy," said the Croatian-born Tomljanovic.
"I came here to help the team and ended up doing that so that makes me happy."
The Billie Jean King Cup final is on Saturday.