Alje Schut scored the only goal of the first half just before the half-hour mark, but Tasreeq Morris leveled after a goalmouth scramble. However, Modise then got the winner on 84 minutes.
Brandon Petersen was forced into an early save, with the Ajax goalkeeper doing well to keep out Anthony Laffor’s powerful effort from range in the seventh minute.
However, the two players were then involved in a nasty collision, forcing both to leave the field in the 16th minute.
Substitute goalie Anssi Jaakkola’s first job came on 25 minutes, in it was to pick the ball out the back of the net after Schut had headed home Modise’s freekick.
Sundowns continued to boss the game, with Cuthbert Malajila and Lindokuhle Mbatha guilty of squandering golden opportunities to double the champions’ lead before the break.
Having failed to register a single shot on target in the first-half, Ajax looked a different unit after the break and leveled matters through Morris in the 54th minute.
Mweene’s attempted clearance from a corner fell at Morris’ feet, and the midfielder made no mistake to net his fourth goal of the campaign.
Both teams pressed forward in search of the winner in what a frantic finish to the encounter, with Modise ultimately claiming the spoils for Pitso Mosimane’s men in the 84th minute.
The former Orlando Pirates midfielder nodded home Kuda Mahachi’s cross, but Jaakkola will shoulder a big portion of the blame.
The win moves Downs back into second spot in the standings, 15 points behind leaders Kaizer Chiefs, while the Urban Warriors’ failure to win for the sixth game in succession sees them fall 22 points adrift of the Amakhosi.