Montenegro forward Dejan Damjanovic put the South Korean champions in front in the 39th minute of a game they dominated, with Go Yo-han adding a second two minutes after halftime.
The second leg will take place in Tehran on Wednesday with the winners advancing to a two-legged final where they are likely to face Chinese champions Guangzhou Evergrande, who won the first leg of their semi-final 4-1 away to Kashiwa Reysol on Wednesday.
Esteghlal beat Thai side Buriram United in the quarter-finals last week and opted to head straight to Korea for the last-four clash rather than return home to Iran.
Despite the long preparation time in Korea, Esteghlal struggled to make their mark on a patchy pitch which was not conducive to flowing football as Seoul dominated from the off with Damjanovic looking dangerous.
The pony-tailed forward inevitably made the breakthrough when he was in the right place to prod home from close range after Esteghlal goalkeeper Madhi Rahmati did well to save a header from one of the Montenegrin's team mates.
It should have been 2-0 seconds later but Colombian striker Mauricio Molina lacked composure and blazed over after Rahmati had raced out to block another Seoul effort.
The Iranians, without defender Khosro Heidari through suspension, started the second period no better and Go was allowed far too much time and space to turn on to his favoured right foot in the area and fire home a low shot.
Esteghlal coach Amir Ghalenoei went to his bench to spark a change in proceedings, hauling off former Aston Villa defender Jlloyd Samuel among others and the visitors came close to snatching a crucial away goal in the final 20 minutes.
The Koreans held firm, however, and will perhaps be disappointed that they did not grab a third goal with Molina again guilty of missing the target, this time with a close-range header in the final minutes.