Rovers were the better side in the first half and deservedly led at the interval through Gael Givet's stunning strike.
But Heskey levelled matters with his first touch after 59 minutes and then Young struck twice in quick succession to see Villa - last season's beaten finalists - reach the last 16.
Rovers must be sick of the sight of Villa after being knocked out of both domestic cup competitions by them last season.
Villa looked out of sorts in the first 45 minutes as Houllier opted for a 4-3-3 formation with John Carew flanked by Gabriel Agbonlahor and Young.
But they were transformed in the second half with Young in inspired form but midfielder Barry Bannan and defender Carlos Cuellar also made key contributions.
Source: PA
Source: PA