American defender Eric Lichaj made the breakthrough against the visitors from League Two, and Villa sealed their victory when substitute Delfouneso popped up with a second goal two minutes from time.
The visitors had battled hard but Villa's superior class was always evident as they completed a deserved win.
Villa manager Alex McLeish had taken a calculated gamble by drafting in seven fringe players.
Shay Given, Luke Young, James Collins, Stiliyan Petrov. Gabriel Agbonlahor and Emile Heskey were among those rested, while former Manchester City midfielder Stephen Ireland was given an opportunity to establish himself.
Hereford, bottom but one in League Two with only one point from four games, were without Adam Bartlett, Stefan Stam and Benoit Dalibard. They included Joey Heath and James McQuilkin.
The skill of the young Villa side was quickly apparent as they dominated the opening exchanges, with Barry Bannan impressive.
It was the little Scot who set up the first real chance with a defence-splitting pass.
He sent Ireland clear but the Irishman was a little slow despite being given a second chance when goalkeeper David Cornell fumbled his save.
Although they were encouraged by 2,500 travelling fans, Hereford struggled to make an impact as an attacking unit.
Their tall midfielder Harry Pell was the first to provide a test of any sort for Villa goalkeeper Brad Guzan, but his long-range effort posed no real threat.
Hereford's defence produced some dogged resistance as they were repeatedly pegged back by Villa's persistent attack.
Ryan Green came to the Bulls' rescue when he sliced a clearance over the bar from Marc Albrighton's cross to rob the lurking Darren Bent.
Despite their superiority, Villa failed miserably to break down Hereford in the first half. No player was more frustrated than Bent who lacked good service.
Bent did create a chance for Ireland in the 35th minute but the Irishman smashed his close-range shot straight at goalkeeper Cornell, who later made a fine save from a Bent header.
Villa stepped up the pace at the start of the second half but goalkeeper Cornell, on loan from Swansea, maintained his impressive form with an early save from Albrighton.
It was in the 52nd minute that Cornell really distinguished himself with a flying save to his left to tip Charles N'Zogbia's 25-yard effort over the crossbar.
Villa should have broken the stalemate on the hour when Ireland weakly headed wide from Albrighton's right-wing cross.
The home side's game became a little untidy and Hereford gained in confidence to mount some attacks, with Joe Colbeck testing Guzan.
Bent surprisingly made way for Austrian Andreas Weimann in the 72nd minute following an indifferent game from the England striker against Green and Michael Townsend.
The tie became more competitive as Hereford gained in confidence but in the 80th minute Lichaj scored Villa's belated opening goal.
Lichaj was on hand in a goalmouth scramble from Albrighton's corner on the left to force the ball home from close range.
Three minutes from time substitute Delfouneso put the result beyond doubt by adding a second Villa goal with a close-range effort.