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After a goalless first half, Chibuike Ohizu broke the deadlock at the Peter Mokaba Stadium after 52 minutes.
With both teams creating chances to score, it was Thabang Makubo who fired in a spectacular shot for a second goal for Babina Noko in the 84th minute.
And despite the Natal Rich Boys pulling a goal back with five minutes of the match remaining through Nqaba Xulu, an 88th minute Muzeu header secured the win for the home side.
Sekhukhune were the inform team coming into this clash, with two successive Betway Premiership victories while Richards Bay remains winless after their opening eight league games.
Ohizu should have done better with the first real chance of the tie midway through the first half but he placed his header wide of the target.
The Nigerian, however, made no mistake in the early stages of the second period with a fine finish past Ian Otieno as he raced onto a long ball from Nyiko Mobbie.
Makubo scored a spectacular solo goal to seemingly kill off the tie, until Xulu popped up with a late effort for the visitors.
There was a brief moment of concern before Bethel Muzeu put the game to bed with a header from a superb Siphesihle Mkhize cross.