The former Sidmouth spinner bowled 60 overs as England levelled the four-match series in Cape Town.
Backed by a 5,000-strong Barmy Army crowd, Bess's highlight of the game came in the Proteas' second innings when he removed captain Faf du Plessis to leave the hosts on 164-4 and set England on their way to the famous win.
With England trailing 1-0 in the series, captain Joe Root elected to bat first having won the toss, meaning Bess could put his feet up before being dismissed for a duck off the bowling of new Somerset teammate Vernon Philander.
The off-spinner shone during South Africa's innings though, with his bowling helping to tie-up an end and allow James Anderson and Stuart Broad to strike. Bess bowled the most over of any bowlers (27) and went for 62-1 at an economy rate of 2.29 including three maidens.
Speaking on the BBC's Test Match Special podcast after day two, Bess received praise from former England spinner and now Guardian cricket writer Vic Marks, who said his bowling was 'terrific'.
South Africa were all out for 223, 46 runs behind England, and Dominic Sibley's 133* inspired the tourists to a huge lead before the declaration just after lunch on day four.
Bess, sent in as a nightwatchman on the end of day three following Root's dismissal, went for another duck, meaning he ended on a pair with the bat.
However, he again impressed with the ball in the Proteas' second innings, bowling 33 overs for figures of 57-1 at an economy rate of 1.72 with 14 maidens.
But the moment that will live long in the memory of Bess, who was only included on the tour after an illness bug swept through the England camp, came when he secured the vital wicket of du Plessis.
A delivery pitched on the offside was swept by the South African captain straight down the throat of midwicket and into the welcome hands of Joe Denly. Elation for the former Sidmouth spinner and England were well on their way to a famous Test win.
Amongst the Barmy Army support was Devonian Christopher Dean who said: "It was an extraordinary atmosphere to be in. Throughout the five days the support was amazing and then, as the tension built on the final day it was something that those who were there - and I am sure also for the players involved - something that will never be forgotten."