"It's so difficult to play against a team that only wants to close you down, but these are the types of games that win you a World Cup," said defender Dani Carvajal after Diego Costa's rebounded goal took them level with Portugal on top of Group B.
"We had climb our way over a huge hurdle and dig in to get the three points."
Spanish newspaper Mundo Deportivo described the match in Kazan as "a heart attack game" while daily Marca declared: "We suffered but the wall fell down".
AS called Spain "leaders of the rebound" while newspaper Sport thanked the existence of video technology which ruled out a potential Iran equaliser for offside, declaring "Long Live VAR!" on its cover.
Spain coach Fernando Hierro effusively praised his opposite number Carlos Queiroz for turning Iran into the unforgiving unit which so nearly held his side to a draw that would have hit their hopes of getting out of the group.
But Carvajal was less complimentary.
"Everyone can play how they want on a tactical level and close up shop at the back, that's part of the game but to waste time by faking injury for me is not football, it's disloyal to the game," the defender said.
Having drawn 3-3 with Portugal after a stunning hat-trick from Cristiano Ronaldo, Spain would have been forgiven for thinking their hardest test in the group was over, but Iran posed a very different challenge.
Midfielder Isco underlined the importance of the win and said his side better get used to playing teams happy to construct a defensive wall.
"This was practically a final, we had to win at whatever cost after the game with Portugal," he said.
"Every team plays differently, we have to be prepared for every situation. We're happy that we have three points and depend on ourselves to go top and now we face Morocco who will also prove difficult."
(This story has not been edited by Devdiscourse staff and is auto-generated from a syndicated feed.)