Their unity government has been in place since February, but stray incidents of political violence among supporters of Tsvangirai's Movement for Democratic Change (MDC) and Mugabe's Zanu-PF party have continued.
Speaking at the anniversary celebrations, Mugabe, who has used previous anniversaries to attack Tsvangirai, called for "national healing".
"As Zimbabweans, we need to create an environment of tolerance, and treat one another with dignity and decency, irrespective of age, gender, race, ethnicity, tribe, political or religious affiliation," Mugabe said.
"We are grateful that the formation of an inclusive government has allowed the spirit of oneness in which we celebrate our 29th year of independence."
Zimbabwe is in the grip of an economic crisis, ravaged by hyperinflation and an unemployment rate of about 90 per cent. Millions of people need food aid.
Analysts blame the crisis on a land redistribution campaign that Mugabe began in 2000, taking land from mainly white farmers and handing it over to his supporters.
Mugabe, however, blames Western sanctions for his country's economic troubles and used his speech on Saturday to repeat calls for sanctions to be dropped against Zimbabwe.
Hillary Clinton, the US secretary of state, in a message timed to coincide with the anniversary, commended Zimbabwe's unity government but made no mention of when or whether the US would lift sanctions or offer aid to Zimbabwe.
The US state department has lifted a travel advisory that warned Americans against visiting Zimbabwe, but cautioned that the political situation there remains unpredictable and could deteriorate.
Speaking on state television, Tendai Biti, Zimbabwe's finance minister and a top Tsvangirai aide, acknowledged that "toxic issues" divided members of the coalition government.
But he said: "I have no doubt in my mind ... we will turn around the economy."