Spain will meet France in the Davis Cup semi-finals, while Croatia are set for a clash with the United States.
Alexander Zverev was no match for a fit-again Rafael Nadal, who charged around the bullring like a matador in Valencia.
The four Charleston Open semi-finalists will return on Sunday after inclement weather put a stop to play.
Germany, France and Croatia are all well placed to reach the semi-finals of the Davis Cup after day three of the quarter-finals.
United States claimed a 2-0 lead over Belgium in their Davis Cup World Group quarter-final, thanks to John Isner and Sam Querrey.
The three Davis Cup World Group ties in Europe were all level at 1-1 after Friday's action, which featured a comeback win for Rafael Nadal.
After more than two months out with a hip injury, Rafael Nadal looked in fine touch with a straight-sets win over Philipp Kohlschreiber.
Daria Kasatkina – the Russian third seed – cruised past Irina-Camelia Begu 6-2 6-1 in Charleston Thursday.
Rising star Naomi Osaka has opened up on a tough couple of days at the Charleston Open, revealing she feels "so sad right now".
Rafael Nadal stressed he must be "respectful" of the hip injury which kept him sidelined, but is ready to return in the Davis Cup.