Vicente del Bosque's team gave an apparently effortless performance and barely flinched even when the hosts took an early lead through Jakob Jantscher.
It was their eighth win in a row and their 23rd in 24 outings - a run interrupted only by a 2-0 loss to the United States at the Confederations Cup earlier this year.
"We've reached a spectacular standard," said striker David Villa, whose two cleverly taken close range goals on Wednesday took his tally to 35 in 54 internationals.
"But this is today, we'll have to see what happens in June."
David Silva, who set up two goals with defence-splitting passes, added: "It's been a really good game, the truth is that the team is on the way up, I hope we can keep it up for the whole of next year.
"We're enjoying ourselves on the pitch and, when you're enjoying it, things work out well."
Constantini added that his team had failed to make Spain's life more difficult.
"When you're the underdogs and are facing top-level opposition, you have to try and make as few mistakes as possible. We didn't succeed in doing that."
