The hosts took an early lead through a penalty by full-back Masixole Banda but Noel Reid bagged the first try of the contest for the visitors on nine minutes at Nelson Mandela Bay Stadium.
That was converted but there was no further scoring during the first period as defences took over and Leinster led 7-3 at the break.
However, it was one-way traffic after the resumption as Rory O'Loughlin, Jack Conan, Joey Carbery and Dave Kearney scored five-pointers in the second half and Ross Byrne kicked three conversions.
Jacques Nel grabbed a late try for Southern Kings but it was no more than a consolation as the Irish side picked up a bonus point for the efforts.
Leinster's win puts them top of Conference B, with a maximum 15 points, and they will stay in South Africa for their next game against Cheetahs at Free State Stadium in Bloemfontein on September 22.