Omari Mwanahamisi put Tanzania ahead after only 26 minutes and she doubled the lead just before half-time.
Kenya pulled a goal back through Christine Nafula but the 2016 Women's Africa Cup of Nations qualifiers were unable to find an equaliser.
In the play-off for third place, which was also played on Tuesday, Ethiopia thrashed Uganda 4-1.
Tanzania beat Kenya 2-1 on Tuesday to win the inaugural Cecafa Women's Championship in Uganda.