Zambia looked on course to progress following strikes from Barbra Banda, Grace Chanda and Misozi Zulu at Barbourfields Stadium in Bulawayo.
However, Leandra Smeda completed a quick-fire brace in the 78th minute before Rhoda Mulaudzi equalised with two minutes to go.
Interim coach Desiree Ellis's charges then held their nerve in the shootout to seal a memorable fightback.
Banyana will face Zimbabwe in the tournament decider on Sunday at the same venue following the hosts' 4-0 demolition job of Kenya in the semi-finals.