DARWIN, Australia (AFP) - Tennis warhorse Lleyton Hewitt clinched a fighting comeback from 0-2 down to lift Australia into the semi-finals of the Davis Cup in Darwin on Sunday.

The 34-year-old Hewitt, playing in his record 40th Cup tie, sealed a 3-2 victory over Kazakhstan with a gritty 7-6 (7-2), 6-2, 6-3 win in the fifth rubber over Aleksandr Nedovyesov.

It was the first time in 76 years that 28-time champions Australia had clawed back from 0-2 down to win a Davis Cup tie.

"I love the back-against-the-wall situation and that's what we had after day one," he said amid high emotion.

"We rallied together and found a way to win.

"We didn't panic when we were 2-0 down. We're united for the one goal. It's been a lot of fun."

While it was Hewitt, Australia's most successful player in the Davis Cup, who won the final live rubber for his 42nd singles triumph in the team competition, it was Sam Groth who kept the tie alive for his country with a hard-fought 6-3, 7-6 (8-6), 4-6, 7-6 (8-6) win over Mikhail Kukushkin.

The big-serving Groth thundered down 29 aces to just get over the line against the never-say-die Kukushkin in just under three hours on the grass court surface.

Australia's victory sets up a semi-final against either Britain or France.

The host nation looked on the brink of being dumped from the competition when they trailed 0-2 after Friday's singles following defeats for youngsters Thanasi Kokkinakis and Nick Kyrgios.

Hewitt and Groth kept the Australians in the tie with a straight-set doubles win over Andrey Golubev and Nedovyesov on Saturday, setting up a tense final day.

Captain Wally Masur made the big call of bringing in Groth and Hewitt over Kyrgios and Kokkinakis to pull off a famous come-from-behind victory by the team's old stagers.

Hewitt, roared on by the home crowd, never gave Nedovyesov a chance in closing out the final rubber to take his overall Davis Cup win-loss record to 58-19 in his 17th and final year on the circuit before he takes over as Australia's non-playing captain next year.

The world No.68 Groth made a flying start by winning the first two sets before was dragged into a dogfight by Kukushkin before winning two tight tiebreakers to clinch a tie-levelling victory.

"This is the most amazing thing I've ever had in tennis. It's unbelievable," Groth said.

"My serve is something I rely on. It's my biggest strength.

"It came through under pressure, especially in that fourth-set tie-break."

It was heartbreak for Kazakhstan, who were bidding to reach the Davis Cup semi-finals for the first time.