Javad Nekounam’s men began the day in the second place after archrival Persepolis had walked away with a 3-0 win at San’at Naft Abadan on the preceding night to overtake the Blues by two points.
Mehrdad Mohammadi found the net midway through the first half and doubled his side’s lead from the spot five minutes into the second half.
Esteghlal’s third came through Mohammad-Hossein Moradmand’s 76th-minute header, leaving the Blues on their way to a comfortable victory against this year’s surprise package of the Iranian top flight.
However, Shams manager Saeid Daqiqi and his men had other ideas and when substitutes Faraz Emam-Ali and Mojtaba Fakhrian cut the deficit to one goal in the space of two minutes the visiting side seemed to be on course for a sensational comeback at the Azadi Stadium.
Esteghlal still managed to hang on to the narrow advantage to restore the one-point lead over Persepolis with six games to spare.
In Abadan’s Takhti Stadium, Danial Esmaeilifar headed home in the fifth minute before Issa Alekasir’s composed finish in 66th minute, followed by Hossein Kan’anizadegan’s penalty five minutes later, sealed a seventh win in eight league outings for Brazilian coach Osmar Vieira, while under-21 keeper Amir-Reza Rafiei, replacing injured Iranian international Alireza Beiranvand, registered a fourth successive clean sheet in the start to his senior career with the Reds.
The defeat left San’at bottom of the table with 16 points – three points adrift of Nassaji Mazandaran, which ended a 13-game winless run with a massive 1-0 victory over Tractor and caretaker coach Mohammad Nosrati thanks to Mansour Baqeri’s effort from the spot in the second half.
Elsewhere, Esteghlal Khuzestan put in a late fightback to salvage a point in a 2-2 draw at Golgohar Sirjan.
Rising star Saeid Saharkhizan broke the deadlock for the host 10 minutes after the interval and Qaem Eslamikhah’s strike in the final minute of normal time looked to be enough for maximum points, before Golgohar keeper Mohammadreza Akhbari made a mess of saving Iraqi Aso Rostam’s header in the second minute of stoppage time and Mahmoud Motlaqzadeh completed the comeback with a sumptuous volley from the edge of the box two minutes later.
Having spent the best part of the season rock bottom in the table, the southern Iranian Blues are now one point clear of the relegation zone.
In Ahvaz, Saeid Vasei’s second-half strike saw Mes Rafsanjan edge Foolad Khuzestan 1-0 and continue the impressive run since Moharram Navidkia took charge of the bench in the mid-season.
Paykan and Havadar, meanwhile, played to a thrilling 2-2 draw in Tehran.