The Brazilians were desperate for a win following an opening game draw, but instead it was the Urban Warriors who came out on top, courtesy of Travis Graham's second half goal.
Both sides started the game with attacking intent, but neither was able to create decent chances in the wet conditions.
Ajax’s best opportunity saw Keagan Dolly firing over the bar, while for Sundowns Katlego Mashego was unable to keep his volley down.
The second half saw more attacking play, but it was the home team who were to take the lead when Graham fired in a cracking low drive from 20 yards out which gave Sundowns keeper Wayne Sandilands no chance. Nathan Paulse provided the assist.
Downs played with more pace and purpose after the goal as Tebogo Langerman got down the left flank with good effect, but they were unable to create many chances bar a Mame Niang header which went wide.
Ajax could have given themselves a two-goal cushion with 15 minutes left, but Paulse saw his glancing header going over the bar.
Downs continued to commit numbers forward in attack, but captain Teko Modise saw his shot blocked, while in the dying seconds of the game Themba Zwane wasted a glorious chance when he hammered a volley over the bar from right in front of goal.