Despite the disappointing result, Downs still enjoy a three-point lead at the top of the table with 35 points from 17 games.
SuperSport United and Kaizer Chiefs are close behind the Brazilians on 32 points each.
Cosmos still sit in 15th place with 11 points.
With the number of chances they created, Sundowns should really have taken all three points. Katlego Mphela was one of the main culprits, and on 14 minutes sent a volley narrowly wide after a cross from Siyanda Xulu.
Jabulani Shongwe shot wide after good interplay with Teko Modise, before Mphela provided a ball for Lebogang Mokoena, whose shot was beaten away by Avril Phali.
Phali was called into action minutes later, when he tipped Themba Zwane's = curling shot wide.
Anthony Laffor added some energy to the Brazilians when he came on for the lacklustre Elias Pelembe after an hour, and sent in a great cross to an unmarked Mphela in the box, but 'Killer' headed wide.
Nyasha Mushekwi headed wide after a cross from Siyabonga Ngubane cross, and had another shot on moments later but was denied by an on-form Phali.
Matthew Rusike, who made some enterprising runs on the wing in the first half, had Cosmos' best chance half an hour into the match, but his attempt was easily saved by Wayne Sandilands.
Siyabonga Nontshinga could have given Ezenkosi a surprise win in the final seconds, but his shot flew just over the bar.