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.

The study, by the Institute for Fiscal Studies (IFS), added that households actually grew richer during the financial crisis.
But it said that the reason for the growth between 2006-12 was the increase in pension values over the period.
And the slow rate of growth in overall wealth suggested that young people would lag behind earlier generations.
Dave Innes, a research economist at the IFS and an author of the report said: "Despite the financial crisis, household wealth on average increased in real terms over the late 2000s, driven by increases in private pension entitlements."
Households aged between 45-54 saw the biggest increases in their pension wealth which rose on average by Â£38,000 over the period.
Mr Innes added: "Even with these increases in average wealth, working-age households are at risk of being less wealthy at each age than those born a decade earlier."
The report added that the range of experiences among the study group was vast - for example, a quarter of households aged 45-54 saw wealth fall by more than Â£69,000, while a quarter say their wealth increased by more than Â£138,000.
The study also looked at people's attitude towards saving and pensions. 30% of individuals reported saving for an unexpected expense, 23% reported saving for holidays or leisure, 15% for planned expenses, 10% for other people and only 10% to provide a retirement income.
Among households aged 25-34, nearly one-quarter (24%) did not expect to receive any income from the state pension in retirement.
However, one third expected it would be their largest source of income after retirement.
Despite new legislation that automatically enrols workers into workplace pension schemes, nearly half (44%) did not expect to receive any income from a private pension.
Rowena Crawford, a Senior Research Economist at the IFS and another author of the report, said: "It is striking how many individuals do not expect private pensions to have a role in financing their retirement, let alone be their main source of income."
"It will be interesting to see how these attitudes change as auto enrolment into workplace pensions is rolled out."

Party officials opted not to automatically reselect Mohammad Asghar, prompting an open contest.
On Thursday night it was announced Mr Asghar had topped the poll.
A second AM forced to follow the same procedure, William Graham, finished outside the top  four - meaning he is effectively de-selected.
Second on the list will be Laura Anne Jones, previously an AM between 2003-07.
In a statement, Mr Graham said: "Whilst I am personally disappointed that I will not be part of an expanding Welsh Conservative team after the elections in May, I remain as invested as any of my colleagues in the goal of bringing an end to this tired Labour government."
The Conservatives currently hold two of the available four seats in South Wales East.
The 60 AMs include 20 elected via regional lists, aimed to give a fairer reflection of support for each party.
Tanzania beat Kenya 2-1 on Tuesday to win the inaugural Cecafa Women's Championship in Uganda.
[NEXT_CONCEPT]
Young people are on track to be poorer than their parents at every stage of their lives, according to a new report.
[NEXT_CONCEPT]
A Conservative AM forced to face a ballot of party members has come top of the South Wales East regional list for the 2016 assembly election.