The result confirms Canada's place in the quarter-finals, where Spain will hope to join them after Rafael Nadal powered the home nation to a comeback victory over Russia in a tie that finished well into the early hours of the morning.
Earlier on, 150th-ranked Vasek Pospisil had given Canada the perfect start before 20-year-old Denis Shapovalov finished the job to make it two wins from two in Group F.
Davis Cup
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Pospisil, who upset the rankings to beat Fabio Fognini in their opening tie, edged out towering American youngster Reilly Opelka 7-6(5) 7-6(7) to the delight of a vocal Canadian contingent in the stands.
Shapovalov, who reached the Paris Masters final this month and has risen to 15th in the rankings, then beat Taylor Fritz 7-6 6-3 to seal the win.
Oddly the doubles rubber was conceded by the Canadians as three of their players were declared unfit to play, according to an ITF spokesman, so the final result was 2-1 to Canada, the same scoreline by which they beat Italy by Monday.
Tuesday's clash was the first between the north American neighbours since 1965. Canada had lost the last four meetings, all played under the old five-rubber system, 5-0. The U.S. have won a record 32 Davis Cups but not since 2007.
Meanwhile Nick Kyrgios returned from a two-month break to launch Australia's Davis Cup challenge on Tuesday and believes they can win the trophy for the first time since 2003.
Playing his first match since September because of a shoulder problem, the 24-year-old eased to a 6-4 6-4 victory over Colombia's lowly-ranked Alejandro Gonzalez.
Australia's number one Alex de Minaur, 20, then gave them an unassailable 2-0 lead with a 6-4 6-3 win over Daniel Galan before the later doubles rubber.
Lleyton Hewitt's side will play a tough Belgium side in their second Group D match on Wednesday when victory would put them through to the quarter-finals.
"I think we can win it for sure," said Kyrgios, who resisted any of his trademark theatrics as he banged down 16 aces, after his straightforward win at Madrid's La Caja Magica, the venue for the revamped Davis Cup finals featuring 18 nations.
"The way Alex is playing, and I know I can beat every single person in this competition and we've got great doubles players, John Peers, Jordan (Thompson) can play singles and doubles.
"We've got great energy guys like John Millman, we've got good depth."
And in the climax of the day, Nadal punched the air as chants of "Rafa, Rafa" echoed around the arena.
After generally disappointing attendances so far at the glitzy new version of the 119-year-old competition, a sell-out crowd in the cavernous 12,500-seat stadium roared the world number one to a 6-3 7-6(7) win over Russia's Karen Khachanov.
While the reaction to Nadal's victory sounded like Spain had won the old trophy for a sixth time, it actually just levelled the Group B tie at 1-1.
The victory would come shortly before 2 am local time when veteran duo Feliciano Lopez and Marcel Granollers beat Khachanov and Andrey Rublev 6-4 7-6 to clinch a 2-1 win.
With Russia having beaten defending champions Croatia 3-0 on Monday there was some anxiety on the Spain bench when Rublev surged back to beat Wimbledon semi-finalist Roberto Bautista Agut 3-6 6-3 7-6(0) and put them ahead.

Rafael Nadal - Davis Cup

Image credit: Getty Images

That left the 33-year-old Nadal with no margin for error against dangerous world number 17 Khachanov. But if ever there is a man for a crisis it is Nadal.
"The format makes things very difficult because every mistake puts you in a position that you don't want to be," Nadal told reporters, anxiously peering at the television to keep track of his compatriots playing doubles.
"The atmosphere has been amazing. The only negative thing in my opinion is we are just starting the last match at 1 am. That makes big trouble for us, for the players and the people who come to the stadium because tomorrow is a work day."
Spain can reach the quarter-finals on Wednesday by beating Croatia, who axed captain Zeljko Krajan two days before their opening tie and will be without injured talisman Marin Cilic.