The match, played at the National Stadium in Dar Es Salaam, Tanzania, forms part of preparations for both sides ahead of the upcoming Under-17 Africa Cup of Nations in Gabon.
Ibrahim Sulley gave Ghana a first half lead, scoring in the 22 minute, before Edmund Arko Mensah added the second goal from a free-kick in the 76th minute.
The Black Starlets appeared headed for a famous win, but the Serengeti Boys had other ideas when the referee added 10 minutes of injury time.
In the fifth minute of stoppage time, Assad Juma pulled one back for Tanzania when the home side were awarded a penalty.
The Serengeti Boys then drew level through Mukhsin Malima in the last minute of added time.
At the Afcon, Ghana will play in Group A alongside hosts Gabon, Cameroon and Guinea.
The Black Starlets will face Niger in another preparatory game on April 16.