Guzan, who made his first start since 2010 in Friday night's qualifier, was superb.
And the Eagles began the second half brightly with Ambrose twice testing Brad Guzan from long range.
Brad Guzan saved Brian Stock's 30-yarder, but Nathan Delfouneso broke through to nod in Nicky Shorey's cross.
Another Guzan parry fell invitingly and this time Jelavic slotted home into the bottom corner from 10 yards.
And Guzan is likely to provide back-up to 37-year-old Friedel, who made 287 appearances while at Ewood Park.
Jelavic got the ball stuck under his foot yards from goal and saw his two efforts blocked by Guzan.
The impressive midfielder Stock pulled back the trigger from 30 yards but Guzan tipped the ball round the post.
Not only did Guzan clear the ball, Zavala was called for a foul.
McNaughton sent in a cross from out wide and Chopra was afforded plenty of space to head past Guzan at the near post.
Cardiff striker Chopra headed Kevin McNaughton's cross past Hull keeper Brad Guzan from close-range to score his third goal in as many matches.
Pedersen came close to doubling his side's lead after the interval, when his curling effort was pushed away by Brad Guzan.
Brad Guzan, in goal because Tim Howard was injured, slid in the snow after balls like a kid in a park.
Guzan is the second American keeper to sign for Villa this summer, Brad Friedel having completed a move from Blackburn last week.
Vienna continued to press and should have equalised through Jelavic after Guzan parried a spectacular overhead kick from Maierhofer into the Croatian's path.
Guzan, who has won five caps for the USA, had been linked with a number of clubs in Europe but opted for Villa.
When Carlos Salcido lobbed a gorgeous chip shot to Zavala in the 43rd, Guzan ended the threat by coming out and slamming into Zavala.
Mexico had 15 corner kicks, including three in the last two minutes of stoppage time, and Guzan body-blocked a dangerous shot by Angel Reyna.
Guzan is the latest American keeper to move to the Premier League, following in the footsteps of Kasey Keller, Friedel, Tim Howard and Marcus Hahnemann.
The formality thwarted a deal in January, but Guzan has played more international football since then, improving his chances of joining the Birmingham club this time.
In the 28th minute, Jorge Torres Nilo sent a perfect cross in to Chicharito, who was right in front of the goal, just a few feet from Guzan.
Friedel will join another American goalkeeper, Brad Guzan, at Villa.
James Coppinger crossed the ball into the box and picked out Price, and with Delfouneso flapping, he steered a low shot past Guzan into the corner of the net.
But Jelavic, who had scored Rapid's goal in the first leg, scored to put Rapid through on away goals, after keeper Brad Guzan had parried a Stefan Hoffmann shot.
Villa agreed this month to sign Guzan from Major League Soccer's Chivas USA, and a hearing to decide whether he can have a permit has been scheduled for August 1.
Friedel, starting his first cup tie of the season in place of his usual understudy Brad Guzan, could not reach Ambrose's corner and the Austrian midfielder rose to plant his header in the back of the net.
Vienna needed only an away goal to regain the advantage and introduced 6ft 7in striker Stefan Maierhofer, who soon had the ball in the net but saw his effort ruled out for a foul on keeper Bradley Guzan.
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