The world number one's 6-1, 6-4, 6-4 win in Valencia drew the tie level at 2-2, before veteran David Ferrer battled to a marathon 7-6 (7/1), 3-6, 7-6 (7/4), 4-6, 7-5 victory over Philipp Kohlschreiber to finish the job.
Germany team captain Michael Kohlmann said: "This is what the Davis Cup is all about".
Holders France were tied 1-1 with Italy in Genoa and 2005 winners Croatia were also deadlocked against visitors Kazakhstan after a day of thrilling action on indoor red clay in Varazdin.
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Ferrer needed almost five hours to defeat Kohlschreiber 7-6 (1), 3-6, 7-6 (4), 4-6, 7-5 at the packed bull ring in Valencia, guaranteeing Spain's return to the semifinals for the first time since 2012. "I played a solid match. Coming back from injuries is always hard, but it's great to be in front of my crowd on a very memorable day".
On Saturday, Marc Lopez and Feliciano Lopez will face Tim Puetz and Jan-Lennard Struff in the doubles, paving the way for a potential tie-deciding clash between Nadal and 20-year-old Zverev on Sunday.
Spain extended its winning streak at home to 27 ties.
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Defending champions France forged a 2-1 lead against Italy after Nicolas Mahut and Pierre-Hugues Herbert earned a straight sets 6-4, 6-3, 6-1 win over Fabio Fognini and Simone Bolelli. The French came out on top in a dramatic match earlier in the day when Lucas Pouille defeated Andreas Seppi in five sets.
"I didn't even know if I really touched him on the shoulder".
The USA were the first side to book their spot in the last-four of the competition as John Isner and Sam Querrey secured routine singles wins over Belgium's Joris De Loore and Ruben Bemelmans, before Ryan Harrison and Jack Sock completed the rout against last year's beaten finalists in the doubles. "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".
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World No. 1 Nadal had not played since he retired from his Australian Open quarterfinal against Marin Cilic in January with a leg injury, but made light work of Kohlschreiber to draw five-time victor Spain level at 1-1 in the tie. This is very special for David who we all love.