The Tigers, who play in the SCFL premier division, won a penalty shootout 4-2 after holding their National League South visitors to a 0-0 draw.
It means two of the top three sides in Sussex are out before the quarter-finals - with Crawley Town having withdrawn because they could not field a side to visit Eastbourne Town, who get a bye.
But Brighton's under-23s are through - after Chichester City made them fight all the way for a 1-0 victory at Oaklands Park.
Also in the last eight are Horsham, who beat Hastings 3-1 in a step three v step four clash at the Camping World Community Stadium.
The town of Horsham makes up a quarter of the last eight line-up - for Horsham YMCA are also through after a 2-0 win at Mile Oak.
The scheduled tie between Little Common and Three Bridges was postponed because of a waterlogged pitch. Tonught (Weds) step five Bexhill host step three Bognor at The Polegrove, while Worthing host Lewes in an all-Isthmian premier clash on Saturday.
In other local football last night Littlehampton Town's prolific marksman Joe Benn scored another hat-trick as Golds beat AFC Uckfield 6-0 in the RUR Cup at the Sportsfield.