A second half double from Matty Fryatt was enough to settle an untidy match that was played on a very heavy Roots Hall pitch.
League Two Southend, who Brown has starred into the play-off places, gave it everything but and came within a whisker of opening the scoring when Michael Timlin struck the crossbar.
But, in the end, a gulf of 62 places between the two clubs saw Hull progress to tomorrow’s fifth round draw.
Fryatt’s double justified Steve Bruce’s decision to rest many of his first-choice stars, the Tigers manager making nine changes from the team beaten 1-0 by Norwich City a week earlier.
This led to the first half being a dour affair, with the heavy state of the pitch playing a big part in both sides finding it difficult to fashion many openings.
So poor was the fare, in fact, that Steve Harper and Daniel Bentley had just one save of note to make in those opening 45 minutes.
The first of those came on 25 minutes when a long throw by Ryan Leonard was flicked goalwards by Barry Corr and a back-pedalling Harper had to be alert to tip over.
Bentley’s big moment came ten minutes before the interval when george Boyd was released by Yannick Sagbo and the former Peterborough United man rolled an inviting cross for Danny Graham.
The loanee from Sunderland, wanted by Nottingham Forest, had what seemed the simple task of beating Bentley but could only fire straight at the Southend goalkeeper.
Those two efforts apart, there wasn’t much to get the sell-out crowd excited before half-time.
That changed four minutes after the restart when Michael Tomlin latched on to an unfortunate ricochet off Stephen Quinn before hitting a 30-yard thunderbolt that hit the underside of the City crossbar.
Such was the ferocity of the shot, Steve Harper didn’t move but that did mean he was on hand to save Corr’s follow-up with ease.
Stung by that lucky escape, Hull fashioned an opening of their own just before the hour butm again,m Graham’s shot was saved by Bentley.
The Shrimpers’ goalkeeper also kept out a David Meyler shot that took a wicked deflection off George Boyd as the game moved into the final half-hour.
If Southend thought they had weathered the City storm, they were wrong as Fryatt popped up on 63 minutes to finish with aplomb after taking the ball off Graham.
Quinn came close to adding a second before substitute Robbie Brady hit a low shot that Bentley did well to hold low to his left.
The game was then settled in the first minute of stoppage time when Fryatt, after being released by David Meyler, turned Luke Prosser inside out before finishing from a tight angle.