Hwang Ui-jo put the Koreans in front in the 58th minute when a calamitous error in the Iranian defence saw Milad Mohammedi and Morteza Pouralighanji collide as they attempted to reach Lee Yong's punt forward.
With the Iran pair grounded, the Gamba Osaka striker had the time and space to race in on goal and slot past Alireza Beiranvand.
But the Koreans held the lead for just five minutes as Kim Young-gwon deflected a corner from Ahmad Nourollahi beyond goalkeeper Cho Hyun-woo to ensure the game ended in a draw.
Wilmots last month replaced Carlos Queiroz, who helped Iran qualify for the 2014 and 2018 World Cup finals, and notched up his first win in charge last Thursday with a comfortable 5-0 victory over Syria at Tehran's Azadi Stadium.
But the meeting with the Koreans represented the first real test for the former Belgium coach, as both nations gear up for the start of the second phase of Asia's World Cup qualifying campaign, which kicks off in September.
(Reporting by Michael Church; Editing by Hugh Lawson)
