Roberto Bautista Agut replaced Nadal for the Group B tie.
While Nadal's preparations for next week's Australian Open suffered a setback, world number one Novak Djokovic was in fine fettle.
The 33-year-old Serb was at the heart of his team's success over Canada.
He saw off Denis Shapovalov 7-5, 7-5 to draw the Serbs level after Milos Raonic had disposed of Dusan Lajovic in the opening singles match.
Djokovic then linked up with Filip Krajinovic in the doubles for a straight sets win over against Shapovalov and Raonic.
The celebration is on for 🇷🇸 #TeamSerbia#ATPCup | @DjokerNole pic.twitter.com/A6WrXwXfub
— ATPCup (@ATPCup) February 2, 2021
"Filip was the key," said Djokovic. "The way he played was phenomenal.
"He came out with very solid returning. He found his serve, great rhythm. He just played some really key shots in the second set when we needed it the most.”
The victory sent Serbia to the top of Group A, which also includes Germany.
France get their Group C campaign underway on Wednesday against Italy who edged past Austria 2-1.
The winners from the four groups meet in the semi-finals on Saturday.
