Nadal's victory in the first reverse-singles match handed Spain a 3-1 decision over Argentina in Seville, with a scheduled fifth rubber abandoned.
The world No. 2 dropped the first set to fellow former U.S. Open champion del Potro but rebounded to carve out a 1-6, 6-4, 6-1, 7-6 (7-0) victory on the red clay at Olympic Stadium.
It marked Spain's fifth Davis Cup championship in 12 years.
The formerly top-ranked Nadal found found his way in the second set, breaking the Argentine in the 10th game of the stanza, then really turned it on in the third, drilling del Potro in seven games.
The final set went to a tie-breaker, where Nadal bageled del Potro and ended the proceedings on his first match point with a forehand winner.