Luciano Vietto scored twice as Villarreal booked their place in the last 16 of the Europa League.
Preserving a 2-1 lead over Salzburg from their first meeting a week ago, the Yellow Submarine won 3-1 in Austria in order to progress.
Vietto's double turned the tie on its head after Marco Djuricin's goal had put Salzburg in front. The hosts were broken after that and Giovani dos Santos wrapped up an impressive win.
After a sterile start, Salzburg burst into life, opening the scoring 18 minutes in.
Marcel Sabitzer's initial hit crashed into Jaume Costa and fell sweetly for Djuricin, who was on the spot to place a finish into the bottom corner from the edge of the area.
It woke Villarreal up and they came into the game, Vietto heading over from a corner when he could have done better.
He did just that on 33 minutes, though. Having failed from one corner he made amends from the next, rising to meet Jonathan dos Santos' delivery and put his side back in control.
They led 3-2 as a consequence and the onus was back on the home side to attack, but they were stifled well by the Spanish side and it was they who went closest to a second.
Denis Cheryshev found himself in space but was unable to beat Peter Gulacsi with his close-range effort, keeping Salzburg alive.
They tried to make the most of their let-off as Martin Hinteregger got a head in but found Sergio Asenjo an equal of it.
Back at the other end and Gulacsi was back in action, keeping out Tomas Pina, but Salzburg were up for a fight and Sabitzer's close-range hit was shut down.
It was quickly becoming the Sabitzer show as he had two more shots which were blocked en route.
Vietto's aim was correct, though, and he was able to give his side the lead on the night and total command overall with 14 minutes left. Giovani broke clear and, after drawing Gulacsi, squared for the Argentinian who did the rest.
That broke Salzburg's resistance and Giovani put the seal on the win three minutes later, Vietto this time the provider as he crossed for the former Tottenham man to cash in.