Keepers at Bristol Zoo Gardens realised that because 30-year-old Salome was not becoming pregnant by her partner Jock despite regular mating, she must not be ovulating.
A medication named Clomid, which encourages the ovary to release the egg, was smuggled into her food.
Soon afterwards, 24-year- old Jock performed his connubial duties and on December 15 the infant arrived.
Because the keepers do not want to interrupt the mother-baby bond, or enrage Jock, they have not managed actually to study the baby themselves.
They have therefore not yet worked out if it is a boy or a girl - and so have not chosen a name.
Salome gave birth to her first baby when she was at Chessington Zoo in April 1988 and moved to Bristol seven years ago.
Her new arrival has delighted the zoo keepers and given a major boost to international breeding programmes which are trying to ensure the survival of western lowland gorillas, whose numbers in the wild are as little as 110,000.
Dr Jo Gipps, director of Bristol Zoo Gardens, said: 'A captive breeding programme is essential for ensuring the survival of such a significant species.
'Sadly western lowland gorillas are facing serious losses in the wild caused by a number of issues including forest destruction for logging, diseases such as the recent outbreak of ebola and the terrible slaughter of primates for the illegal bushmeat trade.
'Salome's baby represents an important contribution to the next generation of gorillas and hope for the long-term conservation of these incredible creatures.'