The five-time champions were facing relegation from Group One of the Europe/Africa zone following consecutive defeats to Germany, Brazil and Russia in Nadal's absence over the past two years.
However, he and Verdasco had too much class for the Danish duo of Frederik Nielsen and Thomas Kromann as they came from a set down to win 4-6, 6-3, 7-6 (7/4), 6-4.
Nadal and David Ferrer had already given Spain a commanding 2-0 lead on Friday.
"The feelings are good. It is difficult to play on a court completely unknown to us and between us we had the obligation to win," said Nadal.
"It is mission accomplished. In the doubles I think we played well in what was possibly the hardest of the three matches."
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