The man and woman, both in their twenties, were sprawled on a settee at their home at Portslade, East Sussex. They had returned after a Christmas Eve party.
The gas fire was on full and rescuers believe the two had been overcome and killed by carbon monoxide fumes that were leaking from it. Their two-year-old child was staying with the man's parents.
A spokesman at East Sussex police headquarters in Lewes said: "I can only confirm that there has been a very unfortunate tragedy at Portslade and that a couple in their early twenties have been found dead."
Joe Garcia, duty control manager for Sussex Ambulance Service, said the deaths highlighted the dangers of gas heaters that were not serviced regularly.