Olivia Smith opened the scoring in the 15th minute after Stina Blackstenius’ shot was saved, giving the Gunners an early lead.
Gabi Zanotti equalised for Corinthians, but Lotte Wubben-Moy restored Arsenal’s advantage in the second half with a well-placed header.
Late drama saw Vic Albuquerque convert a 96th-minute penalty to send the match into extra-time, but Caitlin Foord struck in the 104th minute to seal victory and make history at home.
Arsenal had several early chances, with Russo, Mead, and Blackstenius all testing Corinthians’ keeper Leticia, while Anneke Borbe made crucial saves.
The win sets up a busy schedule, with WSL action against Manchester City on February 8, followed by a Women’s Champions League quarter-final first leg at OH Leuven on February 11.