The top-ranked tennis star's 6-1, 6-4, 6-4 win in Valencia draws the tie level at 2-2, with Spanish world No. 33 David Ferrer up against Germany's Philipp Kohlschreiber in the fifth and decisive match. "It's always special to play in these arenas", added Nadal, who has played in four of Spain's five Davis Cup-winning teams.
If world number 11 Lucas Pouille beats Fognini in the singles, then France will earn a semi-final spot for the third time in four years.
Holders France took a 2-1 lead in their tie with Italy as Pierre-Hugues Herbert Nicolas Mahut comfortably beat Simone Bolelli and Fabio Fognini 6-4 6-3 6-1. The match that they both played was unbelievable.
"Of course, it's a positive thing to win in straight sets", said Nadal, 31, who has not lost a singles match in the Davis Cup since his 2004 debut and in doubles since 2005. It's a great feeling and very unique to play here in front of my people.
Spain and Germany's tie was the only to go the distance, largely due to the surprising doubles win for Jan-Lennard Struff and Tim Puetz over Feliciano Lopez and Mark Lopez.
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The U.S. duo overcame some nervous moments but were able to win key points in the two tiebreakers to secure a victory to ensure the record 32-times winners advanced to the last four. "We ended up winning a pretty comfortable breaker and from that I felt like we were pretty much on top and we just had to finish it off".
The Davis Cup is usually shown on the BBC but with Great Britain not involved the option to broadcast the quarter-finals wasn't taken up.
World No. 3 Marin Cilic, meanwhile, put the finishing touches to Croatia's 3-1 win over Kazakhstan.
The heavily-favored USA team took a 2-0 lead against a depleted Belgium side on the indoor hard courts in Nashville, Tenn., to come within a point of its first Davis Cup semifinals in six years.
Isner needed three hours and 14 minutes to dispose of world number 319 Joris de Loore 6-3, 6-7, 7-6, 6-4, while world No 14 Querrey beat 110th ranked Ruben Bemelmans 6-1, 7-6, 7-5 in a two-hour long second rubber.