Taremi's header sailed over harmlessly, however, leaving Spain to complete one of their tougher World Cup wins. But Spain struggled when put under any serious pressure; they will still expect to face sterner, more clinical opposition as these weeks go on, and the challenge is both single and urgent.
It was not until the 25th minute that Spain had a shot on target, with Silva sending a free kick straight into the arms of keeper Ali Beiranvand.
Nearly immediately, Spain took the lead through Diego Costa's unintended shot. Though they seemed intent on defence, there were question marks on where the goal would come from, in case the Spaniards managed to score.
55' - GOAL! Iran 0-1 Spain (Costa) Silva drives at the Iran defence and feeds Costa who, back to goal, swivels with the ball as Ramin comes in, deflects the ball back against Costa and the ball shoots past Beiranvand!
Iran had chances of their own as the Asian side thought they had equalized just six minutes after Costa's goal. They will make the last 16 with any kind of positive result against Morocco, but they should be in the last-chance saloon, ruing the carelessness that saw them wobble after Diego Costa's fortunate goal appeared to break the most obdurate of opponents.
Spain and Portugal lead Group B with four points each following their 3-3 draw and 1-0 victories.
Iran on the other hand defended magnificently and kept this Spanish elite attacking unit under wraps for the majority of the game.
A reported 15,000 Iranians made the trip to Kazan and, judging from the deafening, continuous humming of air horns and whistles inside the stadium, each and every one of them - plus some locals cheering on Rubin star Sardar Azmoun - was crammed into the arena.
And for much of this game, the Iranians looked like they could fend off their favored adversaries even as Spain dominated possession and camped out in their attacking third of the field.
Iran coach Carlos Queiroz revealed himself to be a big fan of VAR technology despite the replays having ruled out Ezatolahi's strike because of a marginal offside. With that in mind, an opening draw against Portugal and now a win against Iran would have been considered ideal. Bet on a tie game and tell your friends we told you so.