The visitors trailed 22-10 at the break in Port Elizabeth, where Berton Klaasen, Yaw Penxe and Michael Makase all crossed for the former Super Rugby franchise.
There were further tries for both Klaasen and Penxe after the break, but it was not enough to prevent a rampant Ulster from overpowering their hosts.
Sean Reidy and John Andrew both scored in the first half to keep Ulster in touch and the away team came to life in the second half.
Andrew crossed again and was joined by John Cooney, Andrew Trimble, Clive Ross and Robbie Diack in claiming tries to secure the victory and leave Kings bottom of Group B after eight matches.
— Ulster Rugby (@UlsterRugby) November 4, 2017
Edinburgh are fourth in the group, five points behind second-placed Ulster, after dispatching Ospreys 37-10.
Welshman Jason Tovey dominated the encounter for Edinburgh against his compatriots, scoring one try, converting four and sending over three penalties, as the visitors were held scoreless in the second half.
Edinburgh leave it late, but a late try from Magnus Bradbury seals the bonus-point victory! pic.twitter.com/JgHnCZRNNG
— Edinburgh Rugby (@EdinburghRugby) November 4, 2017
In the other matches on Saturday, tries from Niyi Adeolokun and Tom McCartney helped Connacht see off the visiting Cheetahs 23-15 to record their fourth victory in succession in all competitions.
Cardiff Blues, meanwhile, ran in five tries at home to beat Zebre 37-8.
Photo Getty Images. Caption: Sean Reidy playing for Ulster