The Chiefs cut the Stormers to bits in the final play of the first half and a try was awarded to Marshall after TMO Ben Skeen looked favourably at some inconclusive replays. Cruden kicked a superb goal for a deserved 17-6 lead on the balance of play.
The second stanza started with a sparkling try to the Chiefs from the kick-off which Tawera Kerr Barlow scored after some special play from livewire winger Tim Nanai-Williams.
Up 24-6 the Chiefs should have put the Stormers away but wasted numerous try chances.
Then Gio Aplon showed blinding pace from 52 metres out to score a stunner to close the gap to 24-13. The Stormers were rampant and when replacement Nizaam Kahn scored, with Peter Grant's conversion, the Chiefs led just 24-20 with four minutes left.
But then replacement Tevita Koloamatangi showed great strength to score the match winner and a bonus point before Latimer's memorable finish.
Chiefs 36 (James Lowe, Tom Marshall, Tim Nanai-Williams, Tevita Koloamatangi, Tanerau Latimer tries; Aaron Cruden 4 cons, pen) Stormers 20 (Gio Aplin, Nizaam Kahn tries; Peter Grant 2 cons; Demetri Catrakilis 2 pens;