Nishikori defeated Peter Polansky 6-4, 6-4, 6-4 and Dancevic followed with a 6-4, 7-6 (7-2), 6-1 decision over Go Soeda.
Canada and Japan are playing a first-round Davis Cup series with the winner moving into the quarterfinals in April against either two-time defending champion Czech Republic or the Netherlands.
The series turns to doubles Saturday, with Daniel Nestor and Vasek Pospisil teaming for Canada to go against Yuichi Sugita and Yasutaka Uchiyama. Sunday's schedule has Nishikori opening against Dancevic and Soeda playing Polansky in reverse singles.
Nishikori, at No. 18 the highest ranked player in the series, overcame 65 unforced errors and three dropped service games in beating Polansky. However, he allowed Polansky just 11 winners and finished off six of his nine break chances as he won nearly half (48-of-105) of the points off Polansky's serve.
Dancevic had 16 aces and just 22 unforced errors in his win. He fought off six of the seven break opportunities Soeda managed and wound up with four breaks.
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