Already out of contention for this year's eight-team finals, Australia completed a 3-0 win over Colombia in Saturday's "dead" qualifying tie in Brisbane.
Joint and Birrell both recorded straight-sets singles victories, before Storm Hunter and Ellen Perez finished off the job at Pat Rafter Arena.
Joint opened with a dominant 6-1 6-0 win over Yuliana Monroy, before Birrell powered to a 6-1 6-3 victory against Yuliana Lizarazo to give Australia an unbeatable lead in the best-of-three-match tie.
With successes over Australia and Colombia on Thursday and Friday, Kazakhstan had already progressed to this year's eight-team "World Cup of Tennis" finals in China.
But honour was on the line on Saturday as Hunter and Perez overwhelmed Valentina Mediorreal Arias and Maria Paulina Perez-Garcia 6-0 6-1 in the doubles to complete a 3-0 clean sweep.
Despite missing the finals for the first time in seven years, skipper Sam Stosur said victory over Colombia "without a doubt" left the Australians on a high.
"It's always nice to get wins no matter what the situation," Stosur said.
"All the players today went out there with the thought in the front of their mind that they wanted to finish this weekend on a high, and I think that's exactly how they all played.
"They all played fantastic today, didn't let up. It's not necessarily the easiest thing to do when it's a bit of a dead match.
"But it still means something to all these players representing their country and playing as best they can."
26°C