Fearnley showed great resilience to battle to victory over Frenchman Luka Pavlovic, which set up a meeting with Austria's Jurij Rodionov.
The 25-year-old world number 100 recovered from a break of serve down to take the opening set, and held his nerve in the decider to clinch a 6-4 6-7 (4-7) 6-4 win.
Samuel, bidding to qualify for the US Open for the first time, produced a 4-6 6-4 6-1 victory against fellow Briton Billy Harris.
The 23-year-old, who made his slam debut at this year's French Open, will face Chile's former top-20 player Cristian Garin next.
Wendelken, who has never contested the main draw at an overseas major, saved a match point to come through a three-hour tussle with Switzerland's Remy Bertola.
The 24-year-old, ranked 196th, appeared on the brink of elimination at a set and 5-2 down but eventually clinched a 5-7 7-6 (7-4) 6-4 win. He will face Lithuania's Vilius Gaubas.
However, Katie Swan and Jack Pinnington Jones both missed out.
Swan fell to American Mary Stoiana 6-7 (5-7) 6-3 6-3, while Pinnington Jones lost 2-6 7-6 (8-6) 6-3 to Finland's Otto Virtanen.
Former semi-finalist Grigor Dimitrov will face Virtanen after the 35-year-old maintained his bid for a 15th US Open men's singles appearance with a 7-6 (7-5) 6-4 win over Kazakhstan's Timofey Skatov.
China's Olympic champion Zheng Qinwen, contesting a Grand Slam qualifying event for the first time since 2022, beat France's Clara Burel won 6-1 7-5 to set up a match against Russian Elena Pridankina.
There was also victory for 2019 US Open champion Bianca Andreescu, who will aim to secure a first US Open main draw appearance in two years against Slovenian Tamara Zidansek after defeating Ukraine's Veronika Podre 6-0 6-3.
Fery, meanwhile, continued his US Open preparations by reaching the quarter-finals at the Winston-Salem Open.
The fourth seed beat Dutch qualifier Mees Rottgering 6-3 6-3 to reach the last eight.
Fery is competing in only his second event since his stunning run to the Wimbledon semi-finals in July.
He will face American Aleksandar Kovacevic for a place in the semi-finals.

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