Just after the hour mark, Barry ghosted into a shooting position before beating former Villa goalkeeper Boaz Myhill with a deflected effort from the edge of the penalty area.
The goal was harsh on Hull, who had upped the tempo at the start of the second half and had come close to scoring moments earlier through a Leon Cort header.
However Barry's strike effectively killed the match and, with James Milner marshalling the midfield, the visitors dominated the remainder of the contest.
Villa put Hull under pressure from the opening minutes, as they looked to improve a poor cup record since reaching the final back in 2000.
Gavin McCann fired just wide with a left-footed shot from 18 yards, and then Juan Pablo Angel was harshly denied the opener by the offside flag when he pounced on a loose ball from 12 yards and slotted home.
At the other end Hull felt they should have had a penalty when Barry clattered into Jason Price, and Kevin Ellison fired just wide from 20 yards.
However, the away side started to impose themselves and, after Lee Hendrie had seen his right-footed volley from 12 yards well parried by Myhill, the Hull goalkeeper had to be alert again to deny the excellent Milner from distance.
Just before the break Hull's Craig Fagan was denied by Villa keeper Thomas Sorensen from point-blank range, and moments into the second half a powering header from Cort was bundled off the line.
Villa always looked more dangerous going forward, and after 61 minutes Barry collected a poor clearance from Hull to cut inside two players and score with a deflected right-footed shot from the edge of the area, which flew into the top right-hand corner.
Milner came close with two further opportunities as he fired wide following Angel's lay-off, and then volleyed just over from the edge of the area.
Hull's only real opportunity to equalise came when half-time substitute Stuart Elliott headed Ryan France's cross wide from ten yards, but Villa were comfortable winners in the end.
Hull City - Keith Andrews. The former Wolves midfielder battled throughout the 90 minutes to enhance his burgeoning reputation.
Aston Villa - James Milner. Maintained his recent excellent form with an exhilarating and energetic display.