Ahmed Hayal and Abdullah Deeb fired Jordan into a 2-0 lead after 55 minutes, despite Iran dominating the contest.
Karimi pulled a goal back on 67 minutes with a header, before Mohammad Ghazi rescued a draw with a late equaliser.
“We need to take lessons from the result. Iran played better in the second half but we missed our chances,” Karimi told reporters.
Iran, who have already reached the fourth round of 2014 World Cup qualifiers, face Qatar in Tehran on February 29.
Meanwhile Jordan, who recently re-signed coach Adnan Hamad, have also already secured their passage into the final round of qualifying through Asia.
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