The man, said to be in his 40s and the woman, aged 38, were found dead after powering their generating set inside their one-bedroom apartment.
The neighbours, who sought anonymity, told the News Agency of Nigeria (NAN) that the incident occurred on Monday.
One of the witnesses said that due to electricity outage and a downpour experienced at the time, the deceased resorted to powering their generator inside their bedroom.
The neighbour alleged that the man, married with five children and resident in Lagos with his family, had told his wife that he was going for an "outside work" in Port Harcourt.
Unknown to the wife, the man headed for Port Harcourt to meet with his mistress, who was a lawyer, he said.
"On that fateful day it rained heavily, so they resorted to powering their generator right inside their parlour with the windows closed.
"They must have thought that positioning the generator inside their parlour will not have affected them in the bedroom.
"So between 10am and 6pm, nobody suspected any foul play.
Death in the bedroom
"The nearest neighbour to the victims said that when he experienced discomfort in his house due to the increase in temperature of his wall and smoke, he decided to call the attention of other people.
"When we discovered that the fumes came out from her apartment, we decided to break in." The witness said the living room was covered with heavy and poisonous smoke, and added that the neighbours proceeded to the bedroom to discover the lifeless bodies of the couple.
He said the victims must have fallen asleep when the incident occurred.
"It is unfortunate that adults could be this careless knowing fully well the dangers associated with carbon monoxide." Ben Ugwuegbulam, the Police Public Relations Officer in the state, described the incident as mysterious, saying that investigation is ongoing to unravel the true cause of death.
He said their bodies have been deposited at the Braithwaite Memorial Hospital, awaiting autopsy.
According to Clarkson Omoniwari, a medical doctor, when a person is exposed to carbon monoxide, it displaces oxygen from the haemoglobin, thereby causing heart and respiratory failure.
"When exposed between five to 15 minutes, the heart will no longer pump blood and which eventually leads to brain and respiratory failure." He warned the people to keep their generating sets far away to avoid contact with emitted fumes.