Mugabe, 94, who was ousted by the military in November, made a surprise intervention on the eve of the elections, calling for voters to throw Zanu-PF out of office.
Zimbabwe's generals shocked the world last year when they seized control and ushered Mnangagwa to power after Mugabe allegedly tried to position his wife Grace to be his successor.
Mnangagwa, 75, who promises a fresh start for the country despite being from the Zanu-PF elite, is the front-runner with the advantage of covert military support, a loyal state media and a ruling party that controls government resources.
Zimbabweans voted on Monday in the country's first election since ageing autocrat Robert Mugabe was ousted last year, with the opposition vowing to overcome alleged ballot fraud and defeat the ruling Zanu-PF.
President Emmerson Mnangagwa, Mugabe's former ally in the Zanu-PF party, faces opposition leader Nelson Chamisa of the MDC (Movement for Democratic Change) in a historic vote for the southern African nation.
Long lines of voters waited outside polling stations from morning, with election authorities saying early signs suggested a high turnout nationwide.
"I just have to do this. I have to see a better Zimbabwe for my kids. Things have been tough," Tawanda Petru, 28, an unemployed man voting in Mbare, a low-income district of the capital Harare, told AFP.
"I'm going to vote for Chamisa, for change. I am not afraid, I can tell you."
Mugabe, 94, who was ousted by the military in November, voted at his regular polling station in Harare alongside his wife Grace after making a surprise intervention on the eve of the election to call for voters to reject Zanu-PF.
During a two-hour press conference at his sprawling mansion in Harare, Mugabe had said he might vote for the opposition MDC — underlining Zimbabwe's haywire political scene since his fall.
Mnangagwa, voting in his Kwekwe constituency in central Zimbabwe, said Mugabe had the right to express his mind under the country's new "democratic space". "I am very happy that the process for campaign was peaceful (and) voting today is peaceful," the current president added.
A clean vote?
Mnangagwa, 75, who has promised a fresh start despite being from the Zanu-PF elite, is the election front-runner with the advantage of covert military support, a loyal state media and a ruling party that controls government resources.
The party also holds the majority in the lower house of parliament, which is also up for election.
But Chamisa, a 40-year-old lawyer and pastor, who has performed strongly on the campaign trail, hopes to tap into a young population that could vote for change.
"I have no doubt that by the end of the day today we should be very clear as to an emphatic voice for change, the new, and the young — I represent that," Chamisa said as he voted in Harare, supported by chanting supporters.
He again raised fraud allegations, saying "in the rural areas... if the ballot is a genuine one, not a fake one, victory is certain."
On Twitter, he alleged there was a "deliberate attempt to suppress" voting in urban areas — MDC strongholds.
Zimbabwe's generals shocked the world last year when they briefly seized control and ushered Mnangagwa to power after Mugabe allegedly tried to position Grace to be his successor.
The election is Zimbabwe's first without Mugabe, who led ZANU-PF to power when the country became independent from Britain in 1980 and held office for 37 years.
Elections under Mugabe were marred by fraud and often deadly violence, and this year's campaign has been dogged by accusations the result will be rigged.
The MDC has raised repeated allegations of a flawed electoral roll, ballot paper malpractice, voter intimidation and bias in the Zimbabwe Electoral Commission (ZEC). But campaigning has been relatively unrestricted and peaceful.
A recent Afrobarometer survey of 2,400 people put Mnangagwa on 40 percent and Chamisa on 37 percent, with 20 percent undecided.
Mnangagwa, who is accused of involvement in election violence and fraud under Mugabe, invited international observers — including the previously-banned European Union team — to the poll.
The EU team will deliver a preliminary report later in the week.
Desperate for investment
The UN High Commissioner for Human Rights warned of alleged intimidation and threats of violence in the run-up to polling day, but said it was encouraged to see open rallies and peaceful demonstrations.
The next government must tackle mass unemployment and an economy shattered by the Mugabe-backed seizure of white-owned farms, the collapse of agriculture, hyperinflation and an investment exodus.
Previously solid health and education services are in ruins and millions have fled abroad to seek work.
Life expectancy has only just recovered to its 1985 level of 61 years.
"The governing ZANU-PF party needs to maintain a semblance of free and fair elections in order to attract fresh foreign investment," said the London-based EXX Africa business risk consultancy.
"However, there remain serious concerns over vote credibility."
With 5.6 million registered voters, the results of the presidential, parliamentary and local elections are due by August 4.
"I voted for Mnangagwa. We cannot trust the inexperienced. They will take the country back to ours colonisers," said Robina Mayobiongwe, 80, voting in Lupane in rural west Zimbabwe.
A run-off vote is scheduled for September 8 if no presidential candidate wins at least 50 percent in the first round.