Ashoubi scored the opener in the 36th minute from the penalty spot at the Azadi Stadium on Friday.
Five minutes later Ashoubi doubled the advantage for the Blues from the same spot.
Iman Heidari narrowed the gap to just one goal in the 64th minute.
Like many other Estqlal games this season, however, controversy surrounded the referee's decisions.
Reza Ghyathi, a veteran referee, told IRNA that match official Saeed Bakhshizadeh had made numerous mistakes.
"In the first penalty decision, no foul was committed on Omid Ravankhah and the referee should not have awarded the penalty to the Blues," Ghyathi said.
The expert went on to add that Bakhshizadeh failed to point to the penalty spot when a Shahin striker suffered a foul inside Esteqlal's 18-yard box.
Commenting on Estqlal's second penalty, Ghyathi said, "Farhad Majidi was fouled on outside the 18-yard-box and the match official should not have awarded a second penalty to Esteqlal."
"As a veteran referee I apologize to Shahin Bushehr's fans on behalf of Bakhshizadeh," IRNA quoted Ghyathi as saying on Friday.
This is while head of the Iranian Football Federation Referee Committee had earlier denied claims that Iranian match officials have a tendency to officiate in favor of Esteqlal.
"Our match officials are not small individuals [to take sides]," Masuod Enayat said in October.