Cosmos took the lead in the 24th minute though Mashumba when The Zimbabwean striker came up with a cool finish underneath the diving Sage Stephens to start the scoring.
Ezenkosi then doubled their advantage just before the break, when a rather poor free kick from Thabo Ralebakeng eluded everyone, including the goalkeeper who watched it bounce just in front of him and end up in the back of the net.
The Dube Birds got one back early in the second half when some clever link-up play allowed Siyabonga Nomvethe to break through the Cosmos defence and squeeze it home at the near post.
Ivorian forward Brice Aka then wrapped it up late on by making it four, with Ezenkosi getting three important points on the board and a resounding victory.
The result means that all three teams are now on three points, although Cosmos go top on goal difference. The next game is between Cosmos and Black Leopards on Wednesday.