Defender Danny Gabbidon headed the only goal of the game in the 73rd minute as Hughes' men were made to fight by the npower League One side before booking a fourth-round clash with Chelsea.
Owen Coyle's Bolton took their minds of their serious top-flight survival worries as a strike from Kevin Davies after just 34 seconds paved their way to a straightforward 2-0 win over Macclesfield.
In the Trotters' first game since the sale of star defender Gary Cahill to Chelsea, they went further ahead midway through the first half through Martin Petrov to book a home tie with Premier League rivals Swansea.
Jermaine Beckford scored a stunning hat-trick as Leicester stormed into the fourth round with an emphatic 4-0 victory over shell-shocked Championship rivals Nottingham Forest.
Forest's dismal night began with a George Boateng own goal after just seven minutes before Beckford took control, heading his first on the half-hour and following up with two close-range finishes after the break.
Millwall bounced back from their 6-0 home humbling by Birmingham at the weekend with a 5-0 win over Dagenham & Redbridge. Darius Henderson hit a hat-trick and Harry Kane helped himself to two in a one-sided victory.