The team in yellow opened the scoring in the first half through a stunning set-piece by Thando Mngomeni, with Ajax equalizing early in the second half through Eduardo Ferreira, before Erwin Isaacs scored the winner from the penalty spot.
Played on a calm summer's evening, the match got off to a lively start and nearly produced a goal in the second minute when only a superb finger-tip save by Lee Langeveldt denied Thembinkosi Fanteni adding to his seven League goals with a header from a Brett Evans set piece.
Mngomeni then had two opportunities in quick succession for The Peoples' Team, but on both occasion he hesitated for too long and enabled the Ajax defence to smother his attempted shots.
The mercurial Mngomeni has shown before that he is a player for the big occasion and gave a perfect demonstration of this in the 17 th with a beautifully flighted free kick which dipped over the defensive wall and beyond the reach of a diving Hans Vonk to open the scoring.
Fanteni looked determined to make his mark on his last Cape derby before his departure to Israel and he nearly did this in the 30th minute when he out-jumped the Santos defence to head goal-wards, only to see his header cleared off the line by 19-year old Malawian midfielder Tawonga Chimodzi.
Eight minutes later there was action at the other end of the field when an under-hit back-pass by the normally reliable Ajax centre back Ferreira allowed Eleazar Rodgers a sniff at goal, but fortunately for the Brazilian, Vonk read the situation well and made a point blank save at the feet of the Santos striker.
Just before referee Ace Ncobo signaled the half-time break, Bryce Moon spurned a half chance for the Urban Warriors when he headed over the bar after Langeveldt found himself in no-man's land trying to deal with an Evan's delivery.
Ajax started the second half the stronger team and in the 51st minute Evans was presented with an opportunity almost identical to that which brought Mngomeni's goal, but the Ajax man was unable to replicate the accuracy shown by his Santos counterpart.
While not able to score the equalizer, Evans did however play the role of the provider for the Urban Warriors' only goal of the game when his curling corner was put into the net with a powerful header by Ferreira in the 51 st minute.
The Peoples' Team have however showed some real character in recent weeks and they managed to bounce straight back and reclaim the lead when Isaacs coolly converted from the spot after Nazier Allie had brought down Rodgers inside the box.
While Langeveldt looked outstanding in the save, he was not too commanding of the aerial ball and he had Craig Bianchi to thank for clearing the ball off the line on the hour mark.
From this point onwards, the game was played almost exclusively in the Santos half as Ajax piled on the pressure, looking for the equalizer.
In the 78th minute Fanteni had the ball in the back of the net, but was correctly booked for using his hand.
Mwafulirwa should have made it 2-2 four minutes later, but his close-range effort was not wide enough of Langeveldt, who made a brilliant finger-tip save to deny the Malawian.
Mkhanyiseli Siwahla made a big impact for Ajax after coming off the bench and had the chance to grab an injury-time goal when he burst through on goal, but his shot was fired straight at a grateful Langeveldt.
When fellow substitute Nathan Paulse came even closer for the Urban Warriors after his header flew just over the bar, it seemed as if the football gods were smiling on The Peoples' Team as they went on to record their first League win over their neighbours since the 2003/04 season.