AS Roma forward Sardar Azmoun scored in the sixth minute at the Amman International Stadium. Porto striker Mehdi Taremi netted the second goal in the 28th minute.
Jordan’s Yazan Al Naimat halved the deficit in the 74th minute.
Jordan could have equalized the match in the 90th minute but Ehsan Haddad missed his penalty.
Esteghlal winger Mehrdad Mohammadi netted Iran’s third goal in the injury time.
On Tuesday, Iran will play Qatar, who defeated Iraq 6-5 on penalties, in the final and Jordan face Iraq in the third-place game.
Team Melli won the 2023 CAFA Nations Cup in June and picked up friendly wins against Kenya, Bulgaria and Angola.
Iran prepares for the 2023 AFC Asian Cup, where the team has been drawn in Group C along the UAE, Hong Kong and Palestine.