The Kings could have caused more problems but for poor handling, however they will be buoyed by their performance.
The Chiefs, with Liam Messam celebrating his 100th game, had too much firepower - Lelia Masaga scoring three tries - but the Kings hung in there thanks to good scrambling defence and Demetri Catrakilis' goalkicking.
Their wing, 18-year-old speedster Sergeal Pietersen, scored a popular 90m try just before halftime when capitalising on a misunderstanding between Aaron Cruden and Masaga, and No8 Jacques Englebrecht dived over from close range after Pulu's departure.
Sam Cane scored the other Chiefs try in the second half after replacing the injured Ross Filipo, the No8 limping off with what looked like an ankle injury.
The five competition points, plus the two in the narrow defeat by the Stormers last weekend, in which the Chiefs had two men sinbinned, represents a respectable haul as Rennie's men prepare to travel home to Hamilton. They are second on the table on 17 points, behind the Brumbies - who play the Sharks in Durban overnight - on 18.
Rennie will be happy with the enthusiasm in the first half, but probably not as impressed with the inaccuracy which allowed the Kings - in their debut season - to get a foothold on the game.
On Friday night the Chiefs face the winless Highlanders at Waikato Stadium.
Chiefs 35 (Lelia Masaga 3, Sam Cane tries; Gareth Anscombe 3 cons, 3 pens).
Kings 24 (Sergeal Pietersen, Jacques Englebrecht tries; Demetri Catrakilis con, 4 pens).
Half time: 18-13.