Australia edge France in doubles decider, Canada and Germany win in Davis Cup Finals
Canada also began their quest in confident fashion as singles wins for Denis Shapovalov and Felix Auger-Aliassime assured them of victory in their opening Group D tie against Argentina in Manchester.
Germany posted a 3-0 victory over Slovakia in Zhuhai, China which is hosting the Group C matches.
Australia, the 28-time Davis Cup champions who lost to Italy in the final last year, were given a flying start when Thanasi Kokkinakis battled to a 7-6(4) 7-6(3) win over the higher-ranked Arthur Fils, recovering a 2-4 deficit in the second set.
France responded with their number one Ugo Humbert dispatching Alexei Popyrin 6-3 6-2.
But Australia got the win as Ebden and Purcell teamed up to beat experienced French duo Pierre-Hugues Herbert and Edouard Roger-Vasselin 7-5 5-7 6-3.
It was the third year in a row that Lleyton Hewitt's Australia beat France at the Davis Cup Finals group stage.
Canada, the 2022 Davis Cup champions, beat Argentina 2-1 after left-hander Shapovalov defied his slip down the rankings to beat 31st-ranked Francisco Cerundolo 7-5 6-3.
"I feel great," Shapovalov said. "The last time I played in the Davis Cup we won it so it was nice to be back and playing at such a high level."
Auger-Aliassime was then equally assured in a 6-3 6-3 victory over Sebastian Baez to put Canada 2-0 ahead.
Argentina managed to get on the board in the doubles.
Germany proved far too good for Slovakia as Maximilian Marterer beat Lukas Klein 6-4 7-5 before Yannick Hanfmann beat Jozef Kovalik 3-6 6-3 7-6(3). Tim Puetz and Kevin Krawietz then completed the job with a doubles victory.
Sixteen nations are competing in four groups in Manchester, Bologna, Valencia and Zhuhai with the top two from each group moving through to the Davis Cup Final 8 Knockout Stage which is being held in Malaga, Spain in November.
In the day's other tie Belgium beat the Netherlands 2-1 in Group A being hosted in Bologna.
Reigning champions Italy begin their quest in Group A on Wednesday against Brazil although they will be without newly-crowned US Open champion Jannik Sinner.