Australia took the deciding doubles rubber to beat France 2-1 in the Davis Cup group stage in Hamburg on Thursday, while the United States saw off Kazakhstan.
In the second tie in the four-team Group C for both nations, Richard Gasquet gave France the lead when he beat Jason Kubler 6-4, 6-2 in the opening singles.
Alex de Minuar levelled for Australia, beating Benjamin Bonzi 6-3, 1-6, 6-4, before Max Purcell and Matthew Edben won the deciding rubber 6-4, 6-4 against Nicolas Mahut and Arthur Rinderknech.
Australia top the group with two wins out of two, though hosts Germany can draw level if they beat Belgium. France have lost both their ties.
The Americans did not allow a late finish to their opening tie against Britain in the early hours of Thursday morning affect them against Kazakhstan in Group D.
Tommy Paul thrashed Mikhail Kukushkin 6-1, 6-4 in Glasgow to put the US ahead, before Taylor Fritz clinched their second straight win by edging a dramatic contest with Alexander Bublik.
The world number 12 saved four set points in the first set en route to a 7-6 (8/6), 1-6, 6-3 victory.
"Last night was a tough one, and after getting that win it was important to build on that and hopefully not be here again at 1am," Fritz told daviscupfinals.com.
"Any time I play Alex is really tough. He's just awkward to play against.
"I rebounded in the third, changed my strategy a bit, and got the win."
Bublik and Aleksandr Nedovyesov gave the Kazakhs a consolation doubles success by beating Rajeev Ram and Jack Sock, whose late-night triumph had downed Britain, 6-2, 7-6 (8/6).
Elsewhere, Serbia bounced back from their opening loss to Spain in Group B by beating South Korea, with wins for Dusan Lajovic and Miomir Kecmanovic giving them an unassailable 2-0 lead ahead of the doubles in Valencia.
Nam Ji-sung and Song Min-kyu cruised past Nikola Cacic and Filip Krajinovic in the doubles to give the Koreans a match win.
Lajovic played the opening singles rubber having played the doubles against Spain the previous day, also not finishing until gone midnight.
"It definitely wasn't easy. We didn't know who was going to play the singles," he said.
"I went to bed at 4am. I didn't sleep well."
Croatia also managed to put a defeat behind them with a tense success against Sweden.
Eilas Ymer beat Borna Gojo in straight sets to put Sweden, who beat Argentina in the first Group A tie, ahead.
But Cincinnati Masters champion Borna Coric beat Elias' brother Mikael Ymer in three sets and Nikola Mektic and Mate Pavic completed the comeback by seeing off the Ymers 7-5, 6-3.