Iran Press/ West Asia: Yazan Al-Naimat put Jordan ahead at the start of the second half with a clever dink, before Tamari doubled their lead with a superb solo effort.
Jordan had never gone beyond the quarter-finals before this year's tournament.
They will face hosts Qatar or Iran in Saturday's final.
With Bayern Munich's Kim Min-jae absent through suspension, South Korea's defense struggled to cope with a high-pressing Jordan side in the opening half.
Son Heung-min found the back of the net with a clever chip over Yazeed Abulaila, but the Tottenham forward had mistimed his run into the box and the goal was quickly ruled out for offside.
South Korea grew into the game and were awarded a penalty in the 29th minute when Yazan Al-Arab was judged to have brought down Seol Young-woo in the area.
However, the video assistant referee intervened to show it was Seol who had committed the foul and the decision was overturned.
Jurgen Klinsmann's side were undone early in the second half when Kim Young-gwon's sloppy pass was pounced upon by Tamari and played into Al-Naimat, who calmly dinked it over South Korea keeper Jo Hyeon-woo.
Tamari doubled the Jordanians' lead 13 minutes later when he cut in from the right and dribbled past a host of South Korea defenders before passing a low curling strike into the bottom corner of the net.
South Korea, who last won the Asian Cup in 1960, had made it into the last four by scoring stoppage-time goals, but they were unable to find quality in the dying moments this time at Ahmad bin Ali Stadium.
The defeat will see attention fall on manager Klinsmann, who was appointed a year ago and is unpopular with some Korean fans.
214
Read More:
Podcast: Iran knocks out Japan to reach semi-finals at Asian Cup
