The victory moves Al Jazira to nine points from three games, five points clear on top of Group A, as they bid to become the first Emirati side to reach the knockout phase since 2007.
The triumph in Tehran was all the more special, considering it was Esteghlal's first ever home defeat in the ACL.
"I am proud of my team, because this is the first time a team from UAE could gain a victory on Iranian soil," Caio Junior told reporters.
"I am completely satisfied from the result. My players played as they were expected and they were loyal to the team tactics. They played very well and I congratulate them.
"Esteghlal are a very good team and I respect them as I expect to have a tough match against them in the Emirates in two weeks time.
"They are well organised but we worked on their strong points and we were able to contain them very well."
The result boosts Al Jazira's bid to reach the final 16, having failed in the group stage last season, only claiming one point.
Meanwhile, Esteghlal boss Parviz Mazloomi rued a result he felt was unfair on his side.
"We didn't deserve this result and I think my players were a little anxious today," he said.