Goals from the foreign trio of Mor Diouf, Felix Obada and Prince Olomu ensured the Team of Choice ended a six-game winless run in the League.
Ezenkosi, for whom El-Hadji Samb scored a consolation goal, remain bottom of the log.
After a strong start from Cosmos, in particular Siyabonga Nontshinga, Maritzburg gradually took hold of the game.
Cosmos needed goalkeeper Avril Phali to make a handful of good saves to deny the likes of Diyo Sibisi, Michael Morton and Mor Diouf, while the woodwork also came to the visitors' rescue on a couple of occasions.
Finally, just a couple of minutes before half-time, Senegalese defender Diouf demonstrated his aerial prowess with a towering header from a corner kick to put the home side 1-0 up.
After a fairly uneventful first 20 minutes of the second half United doubled their advantage, with winger Obada scoring from a long-range shot that took a big deflection off Cosmos defender Ofusu Appiah and cruelly wrong-footed Phali.
Cosmos pulled a goal back in the 78th minute when Samb crashed home a shot after good set-up play by substitute Alton Meiring, but any hopes they had of a comeback were soon snuffed out by Olomu, who finished neatly past the advancing Phali to make it 3-1 with 10 minutes to play.