Roberto Bautista Agut, who played three days after the death of his father, gave Spain a 1-0 lead by beating Felix Auger-Aliassime 7-6 (3), 6-3 in the first singles match at a packed Caja Magica.
Nadal saved a set point in the second-set tiebreak before claiming his 29th successive Davis Cup singles win - his eighth win out of eight games in a gruelling week for the veteran.
The Spanish crowd that created a wild atmosphere on centre court erupted when Nadal seized his third match point to win the inaugural Davis Cup Finals with an insurmountable 2-0 lead.
The top-ranked Nadal won all of his eight matches at the revamped competition that debuted a World Cup-style format thought up by Barcelona superstar Gerard Pique.
Their 2019 triumph adds to previous Davis Cup wins in 2000, 2004, 2008, 2009 and 2011.
It also completes a phenomenal year for Nadal, who won the French Open and the US Open, all of which helped him to end the year as world No 1 ranking.