Throughout the match, the Chiefs were buoyed by their forwards. Brodie Retallick was immense at lock, summing up his impact by securing the match-winning turnover; and blindside flanker Luke Jacobson seemed to be everywhere on both sides of the ball.
And while their attack was still lacking a certain punch to it, the Chiefs got the result they showed up for to stay in touch with the conference leaders.
The side should really have gone ahead inside 10 minutes with the Stormers under heavy pressure, but missed opportunities saw them trail early on.
Damian Willemse opened the scoring off the tee for the Stormers. The Chiefs hit back through Anton Lienert-Brown who was put away untouched from a lovely offload by winger Solomon Alaimalo to dot in his 50th Super Rugby appearance.
It was about the only bright spot of a forgettable first 40 minutes, and little changed after halftime.
The Chiefs again found themselves behind after putting the Stormers under the pump - again from Willemse's boot, before the pack turned the match.
After sustained pressure deep in the Stormers territory, the Chiefs scrum earned a penalty try. The teams traded penalties after the try, but the Chiefs secured the win and remain well in the hunt for the playoffs.
Chiefs 15
(Penalty, Anton Lienert-Brown tries; Damian McKenzie pen)
Stormers 9
(Damian Willemse 2 pens; SP Marais pen)