But Petric added a second for Bruno Labbadia's side with a fantastic overhead kick on 35 minutes.
Paolo Guerrero - who was banned for five Bundesliga games on Thursday by the German Football Association for throwing a bottle at a fan at the end of his side's 0-0 draw with Hannover on Sunday - rounded off the scoring in injury time with a finish which went in off the post.
In Madrid, Atletico withstood intense late pressure against Valencia but ultimately went through by virtue of the away goals in last week's 2-2 draw.
The home team had the better of the chances until the final 10 minutes.
Striker Villa hit the underside of the bar with only David de Gea to beat before the goalkeeper made a reaction save from Nicola Zigic's point-blank header and then tipped over another effort.
Valencia"s Serbian forward Nikola Zigic felt his shirt had been pulled in the area
But there was controversy as Valencia had a penalty shout turned away in the 85th minute when Zigic appeared to be hauled down by Antonio Lopez inside the area.
Valencia coach Unai Emery was sent off for protesting against the decision, with Zigic running over to the goal-line referee to show off his shirt, which had an enormous hole across his chest.
The striker played the final minutes with a ripped shirt from that incident.
Atletico will be without striker Sergio Aguero for the first leg against Liverpool after the striker picked up a pointless yellow card for time wasting as he was substituted in the 94th minute.
Earlier in the second-half, Atletico's Diego Forlan had hit the post.
The home team have not won a trophy in 14 years, but are still competing on two fronts as they face Sevilla in the Copa del Rey final.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.