Pietersen kicked three penalties to give Stormers a nine-point advantage before Lambie cut the deficit only for Stormers to go 13 points clear when De Jongh dived over.
Flank Michael Rhodes won a line-out at the tail and his burst forward set in motion a handling move that ended with a clever off-load from captain and center Jean de Villiers for De Jongh to score.
A second Lambie penalty left 10 points between the teams at the break and the game was won and lost during the first 20 minutes of the second half.
Pietersen kicked two penalties and Lambie three during the half to give the Stormers a crucial win in their bid to make the play-offs.
FORCE 16, CRUSADERS 14
In Perth, Australia, former Wallaby Sam Norton-Knight scored the Western Force’s only try for a 16-8 half-time lead before the home side held on for a narrow win on Saturday over the Crusaders.
With the Force leading seven-time champions Crusaders with five minutes remaining, Crusaders center Ryan Crotty tackled one of the fans who ran onto the ground.
Flyhalf Jayden Hayward kicked a conversion and three penalties to provide the bulk of the points for the Force, while Luke Romano scored the Crusaders’ only try and Tyler Bleyendaal added three penalties.