Denny Landzaat fired Twente ahead with a 16th minute penalty but Steve McClaren's side paid the price for fielding a second-string line-up and ending the match with nine men.
After Dedryck Boyata was sent off midway through the first half, Joey Brock levelled the score with a deflected shot seven minutes before the break.
Tom van Weert struck from close range to put Den Bosch following the interval before Twente's miserable day was completed when Castagnos was dismissed in the dying minutes following a second booking.
Feyenoord struggled to make an impact against amateur neighbours Xerxes DZB Rotterdam before an own goal by Anthony Bentem broke the deadlock.
Terence Kongolo, Ruud Vormer and Lex Immers completed the 4-0 rout to earn a spot in the last 16.
Central defender Ramon Zomer scored midway through the second half to help Heerenveen squeeze past amateurs Hollandia Hoorn 1-0, while Johann Gudmundsson and Jozy Altidore inspired AZ Alkmaar to 4-1 win at Sneek Zwart Wit.
On Wednesday Ajax, PSV Eindhoven and Vitesse Arnhem secured their spots in the fourth round.
- Sports & Recreation
- Dedryck Boyata