Conrad Madolo scored a superb volley early in the second half to secure progression for the Vultures, who had to withstand late pressure from Ezenkosi to make it through.
United should have broken the deadlock on nine minutes when Tshwarelo Bereng found himself in space, but his shot from a tight angle only found the sidenetting
The visitors created the best chance of the half just before the break when Madolo wriggled past a challenge in the area, but then shot wide.
However, he had his goal soon after - firing home from the edge of the area with a shot that left the keeper no chance.
Cosmos piled on the pressure towards the end of the match, but young goalie Zakhele Ngcobo kept his side in the game and ensured they would be in the quarterfinal draw.