The pair planned to travel from Sheyang in the northeast to Shijiazhuang, south of Beijing, but were barred from the Spring Airlines plane after they informed staff of their status, the Global Times said.
The two, along with an HIV-negative travelling companion, were told that their tickets had been cancelled.
All three sued the budget airline, accusing it of discrimination and demanding an apology as well as compensation of 48,999 yuan (USD 8,000), the paper said.
The two passengers and their friend sought an apology and also compensation
A Shenyang court accepted the case, making it the first lawsuit against an airline for discriminating against an HIV-positive person in China, it added.
"The court's acceptance of this case signalled that HIV carriers can protect their rights through legal channels," it quoted plaintiff Cheng Shuaishuai as saying.
China has a long history of discrimination against those with HIV.
It bans them from becoming civil servants, and they face the possibility of losing their jobs if their employers discover their status, while some have sought hospital treatment only to be turned away.
China only lifted a long-standing ban on HIV-positive foreigners entering the country in 2010.
In recent years top officials have begun speaking more openly about HIV prevention and control, but discrimination remains an issue, with campaign groups and international organisations saying widespread stigmatisation has complicated efforts to curb the spread of the virus.
Under Chinese law air carriers can deny transport to infectious patients, people with mental illness or passengers whose health condition may endanger others or themselves.
Liu Wei, the plaintiffs' lawyer, said that did not mean Spring Airlines had the right to reject the trio, as there was no evidence their presence on board would infect anyone else.
The airline's president Wang Zhenghua told a Chinese media outlet Tuesday that the company did not discriminate against HIV carriers, and blamed the incident on staff anxiety.
But he also blamed the passengers, and said the firm would not deny HIV-positive travellers transport in future, as long as they did not make themselves "overly noticeable" to avoid scaring other customers.
His comments provoked criticism online, with one user of China's Twitter-like Sina Weibo posting: "This fundamentally trampled on human rights.