The world number two, who demolished Juan Monaco in Friday's opening singles rubber on the clay at Seville's Olympic Stadium, gave Spain an unassailable 3-1 lead in the best-of-five tie as the favourites secured their third triumph in four years.
"We gave everything, it was a very emotional victory at the end of a tough year," Nadal said in an interview with Spanish television.
"Winning in this way, we are very grateful to all the people of Spain," he added. "It was the best atmosphere I have experienced in my career."
The lanky Del Potro, who lost a five-set battle with David Ferrer in Friday's singles, thrilled the raucous away supporters with a fearsome display of power hitting to take the first set but lost his way after Nadal levelled at one-all.
The 10-times grand slam champion, undefeated in 16 Davis Cup singles matches on clay, found his range and began spraying crunching winners on both sides of the court with his customary ease.
Del Potro clung on in a nail-biting fourth set and forced a tiebreak when he broke for the eighth time in the match with the Spaniard serving for the title.
Nadal had a near-perfect tiebreak, taking it 7-0, and sealed victory with a trademark forehand winner down the line before embracing his opponent at the net as his Spanish team mates danced on the court nearby.
(Additional reporting by Inmaculada Sanz in Madrid, editing by Clare Fallon)
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