Bea Joy Sagales appeared to be in good health.
Her birth drew applause from others in the airport and military medics who assisted in her delivery.
Her birth was near miraculous - her mother was in an evacuation centre when the storm surge hit and flooded the city.
The mother had to swim and cling to a post to survive, before she found safety at the airport.
Her husband in Manila was unaware of what was happening.
Rescuers face blocked roads and damaged airports as they race to deliver desperately needed tents, food and medicines to the typhoon-devastated area.
Very little assistance had reached the city, residents reported. Some took food, water and consumer goods from abandoned shops and homes.
"This area has been totally ravaged," said Sebastien Sujobert, head of the International Committee of the Red Cross in Tacloban.
"Many lives were lost, a huge number of people are missing, and basic services such as drinking water and electricity have been cut off."
Last night, relief supplies on board a US military plane with a contingent of Marines left Manila for Tacloban.
Josh Morgerman, a member of the storm-chasing group iCyclone, along with colleagues David Reynolds and Mark Thomas, rode out the violent winds before being lifted out on a military aircraft.
Mr Morgerman says his team helped float injured people to safety on mattresses as their hotel was swamped.
Mr Reynolds tweeted: "Wind damage extreme. It's an extremely desperate situation there. We expected bad, but hard to visualise corpses in street, burning city blocks, shell-shocked people, prior to the event."
To donate
Red Cross: redcross.org.nz
World Vision: worldvision.org.nz
Unicef New Zealand: unicef.org.nz
Tear Fund: tearfund.org.nz
Save the Children: savethechildren.org.nz
Oxfam: oxfam.org.nz.
Where to go for help
*The Ministry of Foreign Affairs advises all New Zealanders in affected areas to follow the advice of the local authorities and keep family and friends at home informed of their safety.
* For consular assistance, contact the New Zealand Embassy in Manila on +63-2-891-5358.