Zanu-PF has won the majority of seats in parliament after sweeping rural constituencies by huge margins, official results released by the Zimbabwe Electoral Commission (ZEC) showed.
Preliminary results from the parliamentary vote put Mnangagwa on course of a landmark win in the first election in Zimbabwe since Robert Mugabe was ousted last year after near four decades years in power.
While the electoral commission has five days from the end of voting to release the final tally, the national mood is growing anxious partly because unofficial results are already swirling on social media.
Chamisa, a lawyer and pastor who leads the opposition Movement for Democratic Change party, has claimed victory based on results supporters said they collected from agents in the field.
Nelson Chamisa, 40, and Mnangagwa, 75 were the main contenders in Monday's election, the first since Robert Mugabe was forced to resign after a de facto coup in November after almost 40 years in power.
Police also sealed off roads to the election body's offices as the protesters headed back to the Movement for Democratic Change offices.
"What you see here is real support - not people being brought on buses like ZANU-PF does", he said.
Election observers from the Southern Africa Development Community (SADC) bloc said the vote was peaceful and orderly and opened the door to strengthen the country's democracy.
"We are absolutely confident there was no rigging... we at the Zimbabwean Election Commission will not steal (the people's) choice of leaders, we will not subvert their will", said ZEC chair Priscilla Chigumba.
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Protests by MDC Alliance supporters in the city centre took an ugly turn by the afternoon. "They are stealing our election".
Ballots are still being counted in the presidential election with results expected to be announced later this week.
On the other hand, former Advisor to the late MDC President Alex Magaisa has complained that ZEC's failure to jointly announce Presidential elections results together with House of Assembly is a ploy by the elections management body to rig polls in favour of Mnangagwa.
The predicted outcome was a run-off between the two men with each falling short of the 50 percent plus one vote requirement to win outright.
The crowds chanted: "We want Chamisa".
He accused the commission of releasing the parliamentary results first to prepare Zimbabweans for a Mnangagwa victory.
Whoever wins will face a mass unemployment crisis and an economy shattered by the Mugabe-era seizure of white-owned farms, the collapse of agriculture, hyperinflation and an exodus of investment.
Live video by The Associated Press from Harare shows smoke rising from burning vehicles and opposition supporters scattering after they protested alleged manipulation in Monday's election.