Spain, Belgium, Slovakia, Germany, Russia and Belarus also moved through to the inaugural 12-nation showdown in Budapest.
A weakened Canada, without U.S. Open champion Bianca Andreescu and Eugenie Bouchard for the singles, trailed 2-0 after Friday's action but 17-year-old Fernandez, ranked 185th in the world, beat Bencic 6-2 7-6(3).
It was to be no fairytale comeback though as local favourite Jil Teichmann battled past another Canadian stand-in -- doubles specialist Gaby Dabrowski -- 6-3 6-4 to wrap up a 3-1 win.
Spain raced into the Fed Cup Finals as Carla Suarez Navarro claimed the winning point at the La Manga Club.
The five-times winners led 2-0 overnight and the 31-year-old Suarez Navarro wasted little time finishing off Japan as she swept past Kurumi Nara 6-1 6-3 on the outdoor claycourt.
Nara, 137 on the WTA rankings, was a late stand-in as Japan's number one Naomi Osaka did not take to the court after her dismal defeat by Sara Sorribes Tormo on Friday.
Four-times winners Russia edged out Romania in Cluj as Anna Blinkova and Anna Kalinskaya won the deciding doubles rubber against Jaqueline Adina Cristian and Elena Gabriela Ruse.
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Belgium and Kazakhstan were locked at 1-1 overnight but Elise Mertens beat Yulia Putintseva 6-1 7-6(1) before Kirsten Flipkens secured the winning point by beating Zarina Diyas, also in straight sets in Kortrijk.
Germany were far too strong for Brazil in Florianopolis where Laura Siegemund recorded her second win of the weekend to give her side an unassailable 3-0 lead.
Slovakia ended Britain's hopes in Bratislava where Heather Watson's win in the third rubber gave the visitors a lifeline but Anna Karolina Schmiedlova battled past Harriet Dart to finish the tie off in favour of the hosts.
Belarus squeezed past the Netherlands 3-2 after Aliaksandra Sasnovich and Aryna Sabalenka beat Kiki Bertens and Demi Schuurs 4-6 6-3 7-6(8) in the final doubles thriller.
The United States were 2-0 ahead against Latvia after wins on Friday for newly-crowned featuring Australian Open champion Sofia Kenin and Serena Williams.
France, Australia, Czech Republic and hosts Hungary in the revamped finals taking place in April.
The Fed Cup has followed the men's Davis Cup competition by adopting a multi-nation finals in one city, with 12 team set to assemble at the Laszlo Papp Budapest Sports Arena in April.
They will be split into four groups of three with the winners of each group moving into the semi-finals before a final to decide the 2020 champions.
As well as trying to increase the exposure of the women's team event run by the International Tennis Federation, the extra TV revenue means an $18 million prize fund of which $12 million goes to the players and the other $6 million to the federations.