After seeing off 2021 US Open champion Raducanu on Thursday, Friedsam continued her run with a superb comeback win to book her place in the semi-finals.
A rough start looked to have primed Friedsam for the exit door, but after prevailing in the second set, the 28-year-old pushed on to take herself within a match of a third career WTA Tour-level final.
She will have to wait to discover whether she will face defending champion Jasmine Paolini however, with the Italian's own quarter-final in Portoroz against Katerina Siniakova delayed until Saturday.
Third seed Elena Rybakina, meanwhile, will face Romania's Ana Bogdan after the Wimbledon champion was handed a walkover following Lesia Tsurenko's withdrawal.
Bogdan reached her second tour-level semi-final of the season by upsetting second seed Beatriz Haddad Maia, recording her 20th win over a top-20 opponent in the process, albeit her first since the 2018 Australian Open.
At the Chennai Open, 17-year-old Linda Fruhvirtova stunned Varvara Gracheva 6-4 6-3 to reach her first Tour-level semi-final.
Briton Katie Swan continued her impressive run with a 6-3 3-6 6-3 win over qualifier Nao Hibino and she will face Poland's Magda Linette, the highest-ranked player left in the competition, in the last four.
Fruhvirtova will go up against Nadia Podoroska, who came from a set down to defeat Eugenie Bouchard.
The 2021 US Open champion has faced an uphill battle on the WTA Tour this year and suffered another setback in Portoroz, where she was the top seed, playing the latter two sets with her left thigh strapped after a medical time-out.
A recovery looked possible when Raducanu cruised through a second-set bagel, yet the 19-year-old succumbed in the decider.
Raducanu's defeat follows a first-round exit at Flushing Meadows in a dismal attempt to defend her title.
Friedsman's win, meanwhile, secures the world number 213's first appearance in the quarter-finals of a Tour-level event since she lost in the final of the Lyon Open in 2020. It was also her second victory over Raducanu.
Diane Parry will face Friedsman in the last eight, after she overcame Anastasia Potapova, while Katerina Siniakova – who last week completed a career Grand Slam in doubles at the US Open – defeated Jodie Burrage.
Meanwhile, reigning champion Jasmine Paolini overcame a tie-break finale against Kaja Juvan. The Italian fought back to win 5-7 6-2 7-6 (7-5) to stay on course for a successful title defence.
At the Chennai Open, Anastasia Gasanova failed to back up her first-round win over top seed Alison Riske-Amritraj with another success, as Britain's Katie Swan edged her 7-6 (7-5) 6-2.
That sets up a quarter-final clash with qualifier Nao Hibino.
The top two seeds left in the competition, Magda Linette and Tatjana Maria, also progressed on Thursday.
The Czech secured the third singles triumph of her career – and first since prevailing at Bastad in 2017 – as she recovered from losing the opening set to deny Wimbledon champion Rybakina 6-7 (4-7) 7-6 (7-5) 6-4.
Siniakova – also the doubles world number one – continued her rich vein of form, having captured her third grand slam of 2022 alongside Barbara Krejcikova at the US Open last week.
The world number 82 had come through two matches on Saturday to reach the championship match in Portoroz, and was slow out of the blocks as she fell 5-0 behind in the opening set. Although Siniakova fought back to force the tie-break, Rybakina held her nerve by winning four of the last five points to draw first blood.
The Wimbledon champion, who hit 43 winners, appeared to be closing in on victory in her third final of the year as she broke for 4-3 in the second set. However, Siniakova broke back immediately before eventually forcing a decider.
Both players exchanged breaks early on in the third, but Rybakina's increasing unforced error tally (66) eventually culminated in her opponent claiming another crucial one for 5-4, before serving it out to end the drought.
Over at the Chennai Open, teenager Linda Fruhvirtova also enjoyed a comeback victory as she denied Magda Linette 4-6 6-3 6-4 to land her maiden WTA title.
Aged 17 years and 141 days, Fruhvirtova became the youngest winner on the WTA Tour this season, and is set to climb into the world's top 100 for the first time.
In a tight opening set, Linette broke for 5-4 before holding to love to strike first. A solitary break also proved crucial in the second set; the Czech profiting on this occasion to ensure the final went to a decider.
Linette, who won just two out of nine break points, established early control as she surged into a 4-1 lead, but Fruhvirtova came roaring back as she reeled off five straight games to seal a fitting end to her breakthrough week.
Rybakina, who in July became Kazakhstan's first ever grand slam champion, was too strong for her Czech opponent, creating 14 break point opportunities in the match while only facing two herself.
Her first serve accuracy was not great at 52 per cent, but she was devastating when she landed it fair, converting 21-of-24 chances.
Rybakina will face Lesia Tsurenko in the next round after the Ukrainian upset fifth seed Ekaterina Alexandrova 7-5 7-6 (7-5).
Second seed Beatriz Haddad Maia also had no issue navigating the challenge of Cristina Bucsa 6-1 6-4, and she will meet Ana Bogdan in the third round after the Romanian defeated Tamara Zidansek 6-1 6-7 (7-5) 6-1.
Meanwhile, in India at the Chennai Open, popular Canadian Eugenie Bouchard collected consecutive wins for the first time March 2021 following a lengthy recovery from shoulder surgery.
The 28-year-old defeated Karman Kaur Thandi 6-2 7-6 (7-2) as she looks to climb back up the rankings, currently sitting 902nd in the world after peaking at number five back in 2014.
Earlier in the day, sixth seed Qiang Wang was upset by Japanese qualifier Nao Hibino 6-2 6-3, while fifth seed Rebecca Peterson was also eliminated, going down 6-4 6-2 to Linda Fruhvirtova.
Wrapping up the day's action, Canada's Rebecca Marino booked a potential showdown with third seed Magda Linette after beating Poland's Katarzyna Kawa 7-5 6-3.
