Police described the baby, said to have been in critical condition when it was rushed to the Materno Infantil Hospital in Malaga, as 'stable' in an update around midday.
Receptionist Arturo Bermudez, 40, told how he caught hold of the baby after it 'dropped out' of its mum's womb before performing life-saving CPR.
Mr Bermudez recalled there being little time to call a taxi, forcing him to act on instinct and under the verbal guidance of a 999 telephone operator.
When the ambulance arrived, paramedics took over the rescue efforts and the shocked mother was dashed to hospital.