Alex de Minaur's comeback win was not enough to inspire Australia, as Canada became the first team to book a semi-final berth in Madrid.
Spain will be without Roberto Bautista Agut for the rest of their Davis Cup campaign after the world number nine's father died.
Andy Murray may not feature for Great Britain in Friday's Davis Cup quarter-final tie with Germany, according to captain Leon Smith.
Thanks to Novak Djokovic and Filip Krajinovic, Serbia reached the Davis Cup quarter-finals alongside Great Britain and Germany.
Croatia's hopes of retaining the Davis Cup are over after they were beaten by hosts Spain in Madrid.
The revamped Davis Cup Finals began with defeats for defending champions Croatia and a talented Italy team.
After winning the ATP Finals, Stefanos Tsitsipas feels grand slam success is not far away.