Mehrdad Qanbari gave the home side, which also had a new coach in Saeid Daqiqi on the bench, the lead with 10 minutes into the game but Ramin Rezaeian’s header pulled Mosimane’s men level in the 55th minute.
Masoud Mohebbi slotted home four minutes later to restore the lead for Kheybar before Mohsen Sefid-Choghaei’s smashing strike deep into stoppage time sealed the maximum points for Daqiqi’s side.
Esteghlal, which has now lost five in six outings across all competitions, remains 12th in the table with eight points – three clear of the relegation zone – and with the domestic and continental games coming thick and fast, Mosimane is left with much to do to turn his side’s fortunes around.
Esteghlal will take on Tractor in a highly-anticipated game in the Iranian top flight at home on Thursday before visiting Riyadh to face Saudi heavyweight Al Hilal in the AFC Champions League Elite next Monday.
Elsewhere on Sunday, Persepolis celebrated a fifth successive victory in the league by defeating Shams Azar 2-0 in Tehran.
Ali Alipour bagged his third goal of the season from close range in the 11th minute, smuggling in a Soheil Sahraei’s low cross, before Vahid Amiri’s sensational lob from outside the box in the 91st minute sealed the win for Juan Carlos Garrido’s side.
Persepolis will be back in league action against Esteghlal Khuzestan in Ahvaz on Wednesday and then chase a much-needed first victory in the Champions League when playing Qatari club Al Gharafa in Dubai next week.