Villa were 2-1 winners over Ajax two weeks ago in the first round of group matches and this second victory in the Czech Republic moved them to within touching distance of the next stage.
O'Neill rang the changes following Monday's surprise 2-0 Premier League defeat at the hands of Newcastle United.
American goalkeeper Brad Guzan made only his second appearance for the club, while the likes of regular starters Martin Laursen, Gareth Barry and Nigel Reo-Coker were all rested on the bench.
Steve Sidwell, Moustapha Salifou and Craig Gardner were drafted into midfield and Curtis Davies and Zat Knight formed a new-look central defensive partnership.
The home side were the first to threaten and Guzan was required to palm away a thunderous Jaroslav Cerny drive from 25 yards with 15 minutes on the clock.
Gardner fired a volley from 12 yards straight at the keeper on 20 minutes as he reacted first to a hopeful high ball into the penalty area.
Villa opened the scoring after 26 minutes when Sidwell exchanged passes with Young on the corner of the penalty area before his shot, which the keeper looked to have covered, took a wicked deflection off the body of Carew and spun into the unguarded half of the net.
Young rattled the far post with a free-kick from an acute angle just minutes later as the visitors looked to wrap up the game in the first half.
Home goalkeeper Ladislav Volesak then produced a stunning save to claw out Carew's shot from a pinpoint Young cut-back as Villa threatened to run riot.
Jarolim found the agile Guzan in the way of his 38th minute shot after dancing between two defenders inside the penalty area.
Tomas Necid saw an effort ruled out in the early stages of the second half when the lively striker was correctly flagged offside as he latched on to Jarolim's measured through-ball.
Slavia had the bit between their teeth now and, after Matej Krajcik drilled a low shot across the face of goal, Necid looped a header just wide of the mark.
Villa were content to sit back on their lead as the second half progressed and were lucky when the ball broke to Necid but he could only find the side-netting from a tight angle six yards out.
But the visitors played out the remaining moments without any serious danger and are now in the box seat to qualify for the next stage with two games still remaining.