Bess had already struck twice on the second evening and picked up three more as the Proteas slumped to 113 for five at lunch, 386 behind.
It was an incredible achievement for the Somerset off-spinner, who snared two scalps in 60 overs on his Test recall in Cape Town but headed for the interval with outstanding figures of five for 41.
With South Africa resuming on 60 for two, England captain Joe Root threw the ball to Mark Wood as play got under way and his rapid four-over spell, regularly topping 90mph and threatening the batsman's bodies, provided the perfect contrast to Bess' offerings.
That brought Faf Du Plessis to the crease, in sore need of a captain's innings but only able to produce the briefest of cameos.
He came out with clear intent, drilling Bess for successive boundaries, but when the Englishman adjusted his line he answered by pinging an inside edge to the alert Pope.
Stuart Broad almost had him at short cover on nought, then found himself a few inches away from grabbing a caught and bowled on five.
Bess was wheeling away unchanged at the Duck Pond End in pursuit of his fifth and should have had it when Nortje nicked to slip having made three runs in 62 deliveries. The ball sailed cleanly to Root but he juggled the chance.
Pope failed to hold what would have been his fourth catch under the helmet in Bess' 18th over, when a firm push from Van Der Dussen failed to stick in his outstretched right hand but just two balls later the moment came.
Van Der Dussen, who had started to attack the spinner, went to cut on the back foot but was cramped by the turn and scattered his stumps with a drag-on.
A shower arrived soon after to force an early interval but it would take more than that to dampen English spirits after a rousing session.