Cocciaretto set the tone with a solid 7-5, 6-2 victory over Moyuka Uchijima, edging a tight opening set before building momentum and using her power to pull clear in the second despite a brief fightback by the Japanese player.
Jasmine Paolini then delighted the crowd with a composed 6-3, 6-1 win against Himeno Sakatsume, the world number eight, lifting her level to claim a seventh straight Billie Jean King Cup singles win and leave Italy one step from qualification.
Top-ranked players win
Top-ranked players Elina Svitolina, Belinda Bencic and Linda Noskova were among the winners for their respective countries on a day that saw several surprising results.
Ukraine's world number seven Svitolina sailed past Poland's Katarzyna Kawa 6-2, 6-1, while her partner Marta Kostyuk defeated Magda Linette as they took a 2-0 lead in Gliwice.
World number 14 Noskova of the Czech Republic cancelled out Swiss Bencic’s thrilling opening victory to help the 11-times champions level the tie at 1-1 in Biel.
Noskova beat Viktorija Golubic 6-1, 6-4 after Bencic overcame Marie Bouzkova 6-3, 6-7 (4), 6-4 in a marathon encounter that topped three hours.
Impressive Britain
Britain also made a strong start in Melbourne, taking a 2-0 lead over Australia after impressive wins from 17-year-old debutant Mika Stojsavljevic and Harriet Dart on the opening day.
Stojsavljevic produced a fearless display to beat Australia’s top-ranked player, Talia Gibson, 7-6(4) 7-5, while Dart defeated Kimberly Birrell 4-6, 6-3, 6-3.
In Astana, Canada and Kazakhstan were locked at 1-1 after Bianca Andreescu marked her return to the competition by beating local teenager Sonja Zhiyenbayeva 6-4, 7-6(4).
Yulia Putintseva had earlier given the hosts the lead with a hard-fought 6-3, 7-5 win over Kayla Cross.
Spain's Kaitlin Quevedo and Slovenia's Veronika Erjavec picked up victories for their respective teams as the two nations finished the day in Portoroz tied at 1-1.
The 20-year-old Quevedo won on her debut when Tamara Zidansek retired injured at the start of the third set.
Belgium's Hanne Vandewinkel stunned her higher-ranked US opponent, Iva Jovic, 7-6(3), 6-3, before Elise Mertens defeated McCartney Kessler, who retired with a lower back injury at 3-3 in the decider after a close battle.
Seven nations from the qualifiers advance to the finals, scheduled to take place between September 22nd and 27th in Shenzhen, alongside hosts China, while the losing teams move into the 2026 playoffs later in November.
Catch up with all the results from the Billie Jean King Cup today!