Japanese number one Kei Nishikori was leading 6-2 1-0 on the indoor hard court at Tokyo's Ariake Coliseum when his opponent Frank Dancevic retired with injury, surrendering the tie in their first meeting since 1938.
Nishikori pocketed the first set in 29 minutes and broke Dancevic in the first game of the second when the world number 119 took an injury timeout but could not continue because of a stomach muscle injury.
"The pressure is always on me to win both singles matches," said Nishikori, who won his opening singles against Peter Polansky on Friday before teaming up with Yasutaka Uchiyama to claim Saturday's doubles.
"This time I was able to help win three matches.
"The quarter-finals was our goal after getting back in the World Group. To do it in the first year is very rewarding."
Back in World Group after a one-year absence, Japan now have a perfect 6-0 Davis Cup record against last year's semi-finalists, who were laid low by a spate of injuries.
Their top-ranked player Milos Raonic withdrew on Thursday with a foot injury he sustained at last month's Australian Open, while world number 25 Vasek Pospisil also missed Saturday's doubles with an injury he picked up at Melbourne Park.
Japan will host either Czech Republic or Netherlands in the World Group quarter-finals in April.