The match appeared to be headed for a goalless draw until French striker Jerkovic, who had come on for Milad Midavoodi with nine minutes left, turned the ball in from close range after it had been deflected fortuitously into his path.
It was enough to give Esteghlal, who beat fellow Iran Pro League side Zob Ahan and Saudi Arabia's Al Ettifaq in the play-offs last month to earn a place in Group A, only their third away win in the AFC Champions League and their first victory in Qatar in the competition.
The win also sent the Iran Pro League side three points clear at the top of the group after the match between Nasaf and Al Jazira had been postponed to Wednesday following heavy snowfall in Karshi.
"I am happy with the win against Al Rayyan as Esteghlal scored a goal in the last minute. If we continue to play at this level, we will quality from the group," said Esteghlal coach Parviz Mazloomi.
"Al Rayyan were really good in both halves, and fought very hard."
Prior to Jerkovic's late heroics, the match had been a largely scrappy affair with few real scoring opportunities.
Esteghlal defender Ali Hamoudi was lucky to stay on the pitch in the 30th minute after he was only shown a yellow card for a shocking late challenge on Younes Ali.
And the visitors had a big claim for a penalty five minutes later when Esmaeil Sharifat went down in the box after he tried to get around the challenge of Abdulla Afifa, but all that the Esteghlal player got for his troubles was a yellow card for diving.
Al Rayyan should have taken the lead just before the hour as a swift counter-attack caught the Esteghlal defence cold and as they scrambled to get back in numbers, Rodrigo Tabata's pass found Leandro all alone inside the box but the Brazilian striker could only fire his shot over the crossbar.
With 12 minutes left, Afonso Alves nearly broke the deadlock for the hosts with a shot from just outside the area which took a big deflection off a defender before being magnificently saved by goalkeeper Mahdi Rahmati, who twisted in the air to palm the ball away as it threatened to dip over his head.
But as the match went into stoppage time, it was the visitors who finally struck after a quickly taken free-kick by Hanif Omranzadeh caught out the Al Rayyan defence and Jerkovic turned home from close range after a shot from the edge of the area deflected off an Al Rayyan defender and fell invitingly into the Frenchman's path.
"Everybody has to take responsibility for this defeat," said Al Rayyan coach Diego Aguirre. "I cannot blame the goalkeeper for the goal we conceded, everybody has to take responsibility for this, even me as coach.
"I did not expect to lose this game, but this is what has happened. I felt we could have achieved a win or a draw from this game, but we lost.
"We started very well, but missed chances because we could not focus in the final third."