Messi secured progress from World Cup Group F with his injury-time goal in Manaus, which proved to be the only difference against an impressive and well-organised Iran unit.
Argentina had been frustrated up until that point and Iran even had chances to win the game themselves, with Reza Ghoochannejhad coming close on more than one occasion for the underdogs, who also saw a strong penalty claim turned down.
But, with Messi's heroics for a second successive game, Sabella knows he owes a debt of gratitude to the Barcelona playmaker.
"It was a tough game," he said. " Iran defended well with many people and waited for us but had their chances.
"In the second half we had complications with their counter-attacks, they are a strong and well-worked team.
"But Messi was very strong. He persevered and with him, anything is possible. He is a decisive player. They made the game very difficult for us.
"Messi was marked very tightly, but he showed perseverance, patience, attitude and always looked for the goal. He never gave up."
Despite their own impressive display, Iran finished the game with nothing to show for their performance and now stand on just one point following their first two fixtures.
They face Bosnia-Herzegovina in their final game knowing they need results to fall their way to advance and, while coach Carlos Quieroz was full of praise for Messi, the former Real Madrid boss was scathing of referee Milorad Mazic.
"Messi was fantastic, but the referee wasn't," said Queiroz. "I don't understand it, he had to have seen it was a penalty.
"He was five metres away, there is no way he couldn't have seen it. I have the right to say this and I only hope I am now not punished for telling the truth."
- Sports & Recreation
- Reza Ghoochannejhad