The name Jesus is stamped behind the pulpit in thick blue lettering. But at the Pentecostal Church of the Miracle the headline act is not the Son of God but a six-year-old girl in a pink dress.

A banner advertises "an explosion of miracles" at the entrance to the church – a converted warehouse on the impoverished outskirts of Rio de Janeiro. "She places her hands and the miracle happens." On the roof a placard promises "health, happiness and victory".

On the street outside, anxious followers quiz dapper evangelical doormen: "Is she here? Is she here?"

"She" is Alani dos Santos, a "child healer" better known as the Missionarinha or Little Missionary, who is reputedly capable of healing the sickest of congregants with a touch of her hands. Twice a week, bandage-clad and cancer-ridden believers pack this cramped "temple" in search of a miracle.

"Thousands of people have been touched," says her father, Pastor Adauto Santos, 44, a former hairdresser and car thief who runs what is one of Rio de Janeiro's most talked-about churches and believes his daughter can cure ailments from cancer to Aids and TB.

"She's a normal kid – apart from this gift," he says, adding: "It is Jesus who cures. She is an instrument."

A sensation in the rundown dormitory town of São Gonçalo, the Little Missionary is part of a growing number of infant evangelists in Brazil: child healers, miracle workers and preachers who have become big crowd pullers in this increasingly evangelical nation.

"The Bible itself says that the best praise comes from the mouths of children because they are pure," Santos said. "They sing, they praise, they preach. There are lots of them."

Brazil – and much of Latin America and the Caribbean — is in the midst of what believers proudly call an "evangelical revolution". According to the IBGE, Brazil's census board, the country's Catholic population fell from around 89% in 1980 to 74% in 2000, while its Pentecostal flock grew from 3% to 10%. Brazilian churches are opening branches from Buenos Aires to Port-au-Prince.

The tendency is even likely to play a role in Sunday's presidential election run-off, with the two candidates, Dilma Rousseff and José Serra, openly courting the denomination on issues such as gay marriage and abortion.

Cesar Romero Jacob, a political scientist at Rio's Catholic University, said Brazil's evangelical revolution had gripped two key areas: remote regions in the Amazon and the deprived outskirts of Brazilian cities such as Rio.

A "state vacuum", where poverty, violence, alcoholism and prostitution proliferated, had laid the foundations for the boom. "If the [Catholic] church and the state are absent, somebody else will occupy the space," said Jacob, a leading expert in religious voting trends in Brazil. "Pentecostalism occupied it."

While government neglect has been key to the evangelical explosion, technology is also playing its part.

According to government figures, internet access doubled in Brazil between 2004 and 2009 and the Little Missionary owes much of her success to the web, a place where evangelists gain fame, fortune and sometimes notoriety through homepages and YouTube.

Santos said his daughter's website – where followers can buy a DVD with a "bonus Little Missionary poster" – had received about 2.5m hits from the US, France, China and Japan. "The telephone rings all day," he beamed, before answering a call from a Brazilian TV network keen to interview the Little Missionary. "It's like a call-centre."

The growth of Brazil's evangelical community has bestowed both considerable wealth and political power on many local evangelists.

Bishop Edir Macedo, the leader of the Universal Church of the Kingdom of God and head of one of Brazil's largest TV networks, is widely considered to be the wealthiest bishop on Earth.

Brazilian newspapers estimate that Macedo's estate is worth about $2bn and includes a 35-bedroom mansion in São Paulo and a $50m private jet. Macedo, who claims about eight million followers worldwide, is thought to live in Westchester county, New York state, where the Clinton family were recently reported to be negotiating an $11m mansion.

Jacob said he understood why desperate, "invisible" Brazilians would respond to "those who reached out".

"They are mothers who are worried about their husbands becoming alcoholics, their daughters becoming prostitutes or their sons becoming drug traffickers," he said. "[The church] helps to hold their family nucleus together."

Child curers and the wider Pentecostal church represented a possible form of salvation, he said.

While many question why Brazil's poorest citizens should pay a tenth of their meagre wages to churches, Jacob said the decision was often pragmatic.

"My theory is that people are paying to be citizens in a place where they can," he said. "In this environment people feel they are someone. It is a form of leisure, a place where you can find work, where you feel protected."

At the Church of the Miracle it is also about God-sent cures, and lots of them. Dozens of worshippers arrived at a recent afternoon service using wheelchairs or crutches. Plastic chairs spilled out into the corridor as congregants jostled for a better view. "She is here today to place her little hands on you," Santos told the 200-strong congregation. "Hallelujah," they cheered back.

Rosane Braga, 53, had brought her elderly aunt, Cleonice, who has cancer. "In the name of Jesus [my aunt] will be cured," she said. "Having a child that is being used by God is something sublime, pure, something saintly."

Hunched over in his wheelchair Luiz Gonzaga, 78, said: "It was great. I'm coming every week." Nearby a woman fiddled with a supermarket bag containing syringes and a white box inscribed with the words "Pentecostal Dialysis".

"Some people come here in wheelchairs and leave running," one preacher boasted, shortly before the collection was announced and dozens of golden envelopes filled with bundles of R$20 notes (worth about £7).

Opposition to Brazil's evangelical preachers and the use of infant evangelists is widespread. Some denounce child exploitation. Others cry charlatanism. In his nightly sermons, Santos tackles such criticism head-on.

"How could I pay everyone [to fake a miracle cure]?" he shouted. "Imagine if I gave R$50 to everyone here! I'd need a very big businessman bankrolling the ministry.

"You will hear people criticising," he added. "But it doesn't matter. What is important is what Jesus Christ is doing."

For now such debates are lost on the Little Missionary. "I want to be a doctor," she said, clutching a chocolate rose given by a fan. Why? "So I can keep healing people."