But Hierro insists the problems posed by Iran - who thought they had equalised only for Saeid Ezatolahi's effort to be ruled out by the video assistant referee - indicate there can be no guarantees in Russian Federation.
It was far from a handsome win, but the goal was enough to make Spain coach Fernando Hierro smile.
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Iran started the second round of fixtures top of Group B having beaten Morocco in their opening game, while Spain needed a win after a thrilling 3-3 tie with Portugal.
The Asian side nearly scored the most unlikely of openers when Karim Ansarifard's instinctive effort from a corner flashed into David De Gea's side netting.
Time and time again we've seen goalkeepers come off their lines time in a bid to be their team's hero and score the goal they so desperately need. Fubo TV also offers three days of auto recording and 30 hours of Cloud DVR service in case you're busy at work for the Spain Iran soccer game.
Iran continued to push hard and managed to challenge with some fast counterattacks.More news: Fighting rages around airport in Yemen port city of Hodeida
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Queiroz's troops continued to threaten as the second half went on, with Mehdi Taremi heading over the crossbar at the far post on 81 minutes.
First place in the group could be decided by goal difference.
Iran, with a victory over Morocco in the first round of pool play, remain in contention to advance to the knockout stage, but the African nation is now only playing for pride with just one match to come, against Spain.
Moments later, the stadium erupted when Ezatolahi fired through a packed Spain area to beat De Gea but the assistant referee's flag was up.
Iran was risky from set pieces and its restless defensive display was impressive. "It was hard for us to create chances".
Costa had a bust-up with Beiranvand toward the end of the first half after the Iran keeper went down in the box.
"Everybody knows that Spain is one of the greatest teams in football history, and one thing that we can guarantee is that the Spanish team will not have an easy time against us", he told reporters. "We happened to meet at Malaga, then in the national team".