The self-immolations happened on a busy central market street in Tibet's capital city Lhasa, China's state-run news agency Xinhua said.
Policemen put out the flames and the two men quickly were taken to hospital, the Xinhua report said.
"These were the first cases of self-immolation in the capital of the southwest China's Tibet autonomous region, though a spate of similar incidents has occurred in the Tibetan areas of Sichuan, Gansu and Qinghai provinces over the past year," Xinhua said.
A Communist party official condemned the acts, which took place during a Buddhist festival when the streets were crowded with pilgrims.
"They were a continuation of the self-immolations in other Tibetan areas and these acts were all aimed at separating Tibet from China," Hao Peng, secretary of the Commission for Political and Legal Affairs of the Communist Party of China Tibet Committee, said.
Xinhua reported more than 20 Tibetans have died from self-immolation since March 2011. Most of them have been Buddhist monks and nuns. The majority of self-immolations have taken place in the Tibetan areas of Sichuan, Qinghai and Gansu provinces.
"Investigators found that in many cases photos of the designated self-immolaters had been sent in advance to separatist forces abroad, indicating that the self-immolations had been carefully planned," the Xinhua report said.
"After the tragedies, separatist forces would immediately publish these photos alongside pictures of the self-immolation scenes to play up the situation."
The self-immolations have been an embarrassment to the Chinese authorities as they continue their decades-long war of words with the self-exiled Tibetan spiritual leader, the Dalai Lama.
Beijing consistently has fought against what it says is the Dalai Lama's interference in Tibetan affairs since he fled to India soon after the Chinese army marched into Tibet in the late 1950s.
In particular, Beijing says the Dalai Lama urges terrorist acts against Chinese people and institutions in Tibet, as well as encourages acts of self-immolation -- both of which the Dalai Lama denies.
A Xinhua article earlier this month and by-lined by Zhou Yan heavily criticized the Dalai Lama for what the writer said was his failure to condemn self-immolation.
"The so-called spiritual leader of Tibetan Buddhists turned a cold shoulder to the loss of life," Zhou said.
"The Dalai Lama is apparently basking in glory these days, after receiving the $1.77 million Templeton Prize and meeting with British Prime Minister David Cameron, to the indignation and protest of the Chinese government."
Zhou said "the lives of ordinary Tibetans were always considered dirt cheap under the Dalai Lama's rule in old Tibet," a reference to the days prior to Chinese military takeover of Tibet in the mid 1950s.
Beijing's policy has been that Chinese authority over Tibet has raised the living standard of the once feudal land and is welcomed by ordinary Tibetans.
At the beginning of the year, Xinhua reported the Tibet Autonomous Region government had "earmarked more than $1.3 billion this year with much of it for rural infrastructure construction and agricultural subsidies.
The Dalai Lama tries to undermine this progress and "the spate of self-immolations over the past year has served him well by drawing wider international attention," the Xinhua report said.
Instead of denouncing and calling for an end to the suicidal acts that deviate from the tenets of Buddhism, the Dalai Lama praised the "courage" of the self-immolators, Chinese officials said.
In an exclusive interview with the BBC in November, the Dalai Lama denied accusations by Beijing that he actively encourages Tibetans to self-immolate. He questioned the usefulness of the acts as a protest tool against the Chinese authorities and their more than 50 years of rule in Tibet.
"There is courage -- very strong courage" by the people who set themselves on fire. "But how much effect? Courage alone is no substitute. You must utilize your wisdom," he told the BBC.
Notable deaths of 2014 [PHOTOS]