Canada was runners-up three years ago in Madrid, when a 19 year-old Auger-Aliassime and 20 year-old Shapovalov lost their respective singles clashes with Roberto Bautista Agut and Rafael Nadal.
Three years older and three years wiser, this time the Canadians dominated the trophy match at the expense of 28-time champion Australia.
Shapovalov got Canada off to a flying start by crushing Thanasi Kokkinakis 6-2 6-4, setting up the chance for Auger-Aliassime to clinch victory without the need for the contest to go down to a doubles decider.
World number six Auger-Aliassime made no mistake as he fended off Alex de Minaur 6-3 6-4, adding Davis Cup glory to the four singles titles he has gathered this year.
Auger-Aliassime saved three break points in the sixth game of the second set, from 0-40, when a trailing De Minaur was looking to hit back. He then sealed Canada's victory minutes later with a forehand into the corner that his opponent could only return out of court, before being mobbed by team-mates.
Each of Auger-Aliassime's 2022 titles came at indoor hard court events, and he has thrived again in those conditions this week, winning all three of his singles rubbers and a doubles tussle on Saturday against Italy alongside the experienced Vasek Pospisil.
The Canadian pair got the job done just minutes before kick-off time in their country's World Cup game against Croatia.
"The emotions are hard to describe," Auger-Aliassime said. "All of us here, we've dreamt of this moment.
"These guys around me, except Vasek, he's a little bit older than me, we grew up together from the ages of seven, eight years old in Canada dreaming about being on this stage, winning these types of matches, winning a Davis Cup.
"It's really a dream come true, for me personally and I think for all the team. It was a great moment for myself and the country."