On Tuesday's opening day of group stage action, Canada, the 2022 champions, won 2-1 after left-hander Shapovalov defied his slip down the ATP 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.
The South Americans managed to get on the board in the doubles.
Germany posted a 3-0 victory over Slovakia in Zhuhai, which is hosting Group C matches.
The fact the International Tennis Federation (ITF) placed European teams in China has been heavily criticised.
"I think the teams that are here now all agree that it's nonsense to play here," Germany team manager Michael Kohlmann said.
The Germans proved far too good with Maximilian Marterer beating Lukas Klein 6-4 7-5 before Yannick Hanfmann beat Jozef Kovalik 3-6 6-3 7-6 (7-3).
Tim Puetz and Kevin Krawietz then completed the job with a doubles victory.
"I think it's a big relief for us," Marterer said.
"I'm very happy with this start to the week, it makes me want more."
Australia edged out France with Matthew Ebden and Max Purcell claiming the doubles decider in the Group B clash in Valencia, Spain.
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 (7-4) 7-6 (7-3) win over the higher-ranked Arthur Fils.
Thanasi Kokkinakis serves during his win over Arthur Fils in Valencia. (EPA PHOTO)
France responded with their No.1 Ugo Humbert dispatching Alexei Popyrin 6-3 6-2 before Ebden and Purcell teamed up to beat 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 Aussies beat Les Bleus at the Davis Cup Finals group stage.
In the day's other tie, Belgium beat the Netherlands 2-1 in Group A being hosted in Bologna, Italy.
Sixteen nations are competing in four groups, with the top two from each moving through to the Davis Cup Final 8 Knockout Stage which to be held in Malaga, Spain in November.
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.
With DPA.
