After the restart the Chiefs pulled back with a Gareth Anscombe penalty, though the Stormers soon extended their lead with another try when scrumhalf Nic Groom wriggled through the narrowest of gaps to score.
A Pieterson conversion took the lead out to 33-20, but the Chiefs showed their star quality when they scored two converted tries to a solitary Stormers penalty to get themselves to within two again.
Ngatai was set-up by a great break from Anscombe and coasted in before Andrew Horrell went over in the corner for the bonus-point try after some wonderful handling by the backs.
In Port Elizabeth, Patrick Lambie scored all the points for the Coastal Sharks as they ground out a 21-12 victory over the Southern Kings on Saturday in a fiery, tryless Super 15 clash.
The Springbok flyhalf succeeded with his six penalty attempts at a near-full Nelson Mandela Bay Stadium in the Indian Ocean city.