Since being shared on Instagram last week by a doctor at the clinic, the clip has amassed more than 15,000 views.
During what are considered normal C-sections, doctors remove the baby after they have made the small cut.
Babies born this way are susceptible to respiratory problems as they are brought out so quickly that they struggle to adapt to breathing normal air.
But this other method, adopted on film at the Centro de Fertilidad Clinica Lugo in Maracay, saw doctors guide the baby naturally, The Sun reports.
Experts say that slower, natural caesareans reduce any risk and are more beneficial to the mother as she feels more involved.
It can take up to four minutes for the baby to be born during a natural caesarean, before it is placed on the mother's chest, which is thought to help bonding.
In July last year, MailOnline reported on another video of a gentle C-section, filmed in Australia, which went viral.
The clip showed the baby effectively delivering himself, progressively wriggling his way clear of his mother's stomach through an incision made during the caesarean.
Doctors and nurses looked on as the newborn slowly emerges, removing his head followed by his shoulders and then the full body.