(CNN)Judy Murray called it a "Fine Bromance."
Her sons Andy and Jamie don't often get together on the tennis court, but when they do it can be "magic" -- and it helped Great Britain reach the semifinals of the Davis Cup for the first time since 1981.
The brothers, with mom watching, combined in the doubles Saturday to give their country a 2-1 lead in the best-of-five rubber against France at London's Queen's Club.
World No. 3 Andy duly wrapped up victory for Britain and a semifinal with Australia when he beat Gilles Simon in four sets Sunday to give his team an unassailable 3-1 lead in the tie.
But the key to its passage to the last four was the doubles victory.
GB captain Leon Smith paired the brothers together after Andy had won his Friday singles match against Jo-Wilfried Tsonga to level the tie at 1-1 after Simon had beaten James Ward in the opening rubber.
"I didn't care who played as along as we won the match," Jamie Murray said after the 4-6 6-3 7-6 (7-5) 6-1 victory against Tsonga and Nicolas Mahut.
"But to go out there with your brother and play for your country, and having Leon on the bench who has been part of our careers from a young age, it was really special. It was a magic day."
The Scottish siblings last played together at an ATP Tour event in 2013, while their only Davis Cup outing as a doubles duo was four years ago against Luxembourg, when they also won.
"When we play together on the tour, I want to win for Jamie, but for the whole weekend here it's different, you want to win for the whole team," said Andy.
"You want to win for the country as well so it's a bit different. Maybe that helps me a little bit when I play with Jamie in the Davis Cup."
Earlier Sunday, Australia completed a remarkable turn around from 0-2 down against Kazakhstan as veteran Lleyton Hewitt proved the hero.
He paired with big-serving Sam Groth to beat Andrey Golubev and Aleksandr Nedovyesov 6-4 7-6 (7-4) 6-2 in the doubles.
Groth drew the team's level by winning the first reverse singles as he powered 29 aces in a hard-fought 6-3 7-6 (8/6) 4-6 7-6 (8/6) win over Mikhail Kukushkin.
Then Hewitt, who is due to retire in January 2016, repaid the faith put in him by captain Wally Masur with a straight sets 7-6 (7/2), 6-2, 6-3 win in the deciding rubber against Nedovyesov.
"I love the back-against-the-wall situation and that's what we had after day one," Hewitt told the official Davis Cup website after completing Australia's first recovery from 2-0 down in a Davis Cup tie for 76 years.
Meanwhile, Belgium will host Argentina in the other semifinal, to be played September 18-20, after both nations secured unbeatable 3-0 leads.
The Belgians are through to the last four for the first time since 1999 after former French Open junior champion Kimmer Coppejans and Ruben Bemelmans beat Canada's Daniel Nestor and Adil Shamasdin 7-5 3-6 6-4 6-3 in Middelkerke.
In Buenos Aires, Argentina comfortably defeated a Serbia side missing this month's Wimbledon champion and world No. 1 Novak Djokovic.
Carlos Berlocq and Leonardo Mayer thrashed Nenad Zimonjic and Viktor Troicki 6-2 6-4 6-1 on clay to earn a trip to Belgium in what will be the South Americans' 10th semifinal since returning to the World Group in 2002.