Leylah Fernandez sealed Canada's place in the Billie Jean King Cup semi-finals for the first time since 1988, as Italy also reached the last four in Seville.
Fernandez, 21, beat Poland's Magda Linette 6-2 6-3 after Marina Stakusic overcame Magdalena Frech 4-6 7-5 6-3.
Italy are also through to Saturday's semi-finals - for the first time since 2014 - after beating Germany 3-0.
The USA began their campaign by beating defending champions Switzerland, while Australia edged Kazakhstan.
Fernandez prevailed in a three-hour match against Sara Sorribes Tormo, which she described as a "bullfight", to give Canada victory over Spain on Wednesday.
But, a day later, the world number 20 was a comfortable winner over Linette and Fernandez said she was "proud and ecstatic" that her nation had ended a 35-year wait for a semi-final spot.
Team-mates Gabriela Dabrowski and Eugenie Bouchard completed a 3-0 win over Poland - who are without world number one Iga Swiatek - with a 6-2 6-3 win against Weronika Falkowska and Katarzyna Kawa.
Martina Trevisan and Jasmine Paolini confirmed Italy's progress from Group D with singles wins, before Lucia Bronzetti and Elisabetta Cocciaretto edged a match tie-break against Friedsam and Laura Sigemund in the doubles - winning 6-4 6-7 (4-7) 11-9.
Paolini recorded her second singles win of the tournament by beating Friedsam 6-3 6-2 after Trevisan - also backing up her win in the opening 2-1 victory against France - defeated Eva Lys 7-6 6-1.
Record 18-time winners the USA, who would face Group C winners Canada should they top Group A, will aim for a last-four place against the Czech Republic on Friday after overcoming winless Switzerland.
Sofia Kenin, playing her first Billie Jean King Cup tie since 2020, clinched victory by beating Viktorija Golubic 6-3 6-7 (1-7) 7-5 after Danielle Collins won 7-6 (7-4) 6-1 against Celine Naef.
Sloane Stephens and Taylor Townsend ensured a clean sweep for the USA, winning 6-1 7-6 (7-3) against Jil Teichmann and Simona Waltert, as Switzerland's title defence ended with back-to-back 3-0 losses.
In Group B, Australia beat Kazakhstan 2-1 after Storm Hunter and Ellen Perez won a third set match tie-break in their decisive doubles match against Anna Danilina and Yulia Putintseva, prevailing 6-1 4-6 (10-5).
Hunter had put Australia ahead by winning her singles match against Danilina 7-6 (7-2) 6-4 but Putintseva beat Kimberly Birrell 6-0 7-5 to level the tie.
Kazakhstan play Slovenia in their final group match, with Slovenia guaranteed to progress with victory following their opening win over Australia.
What is the Billie Jean King Cup - and when do GB play?
Twelve nations are taking part in the finals of the competition, which was formerly known as the Fed Cup, with teams split into four groups in the round-robin stage.
The group winners will advance to Saturday's semi-finals before the champions are crowned after Sunday's final in Seville.
The winners will receive prize money of $2.4m (£2.1m), which is part of an overall payment pot of $9.6m (£8.4m) - a record figure for the event which matches the cash awarded in the men's equivalent Davis Cup.
Great Britain did not qualify after losing to France in April's qualifying stage, instead going into a play-off tie against Sweden in London on 11-12 November.
Led by Katie Boulter, GB face Sweden a the Copper Box Arena with a place in next year's BJK Cup qualifiers at stake.
The tie, which consists of five matches - four singles contests, with a deciding doubles if needed - will be shown live on BBC Sport.