The victory extended Sundowns' unbeaten league start and stretched their remarkable home run to 32 matches without defeat. They are now level on 10 points with leaders Orlando Pirates after four games.
Sundowns took control before the break with two outstanding finishes. Brayan Leon opened the scoring midway through the first half, volleying into the top corner after Cassius Mailula's effort took a deflection into his path.
Teboho Mokoena then marked his return from injury in spectacular fashion, curling a free-kick from outside the box into the top corner to double the advantage.
AmaZulu coach Arthur Zwane responded with changes before and during half-time, and the visitors immediately gave Sundowns something to worry about. Thandolwenkosi Ngwenya reduced the deficit shortly after the restart when he got on the end of Riaan Hanamub's cross.
Ngwenya, who has now scored in all five of AmaZulu's matches this season across all competitions, would later add another to take his tally to seven goals.
Sundowns, however, quickly restored their two-goal cushion. AmaZulu goalkeeper Faveur Kouassi could only parry an effort into the path of Tashreeq Matthews, who calmly finished into an unguarded net.
The hosts then exploited further gaps in the AmaZulu defence. Matthews struck the upright before the rebound eventually allowed Leon to complete his brace and put Sundowns 4-1 ahead.
Ngwenya refused to give up and pulled another goal back in the 70th minute after Ronwen Williams ventured too far from his area, but Sundowns remained in control.
Bennet Mokoena completed the scoring in the final stages to seal a convincing win.
While Miguel Cardoso will be pleased with the attacking display and Mokoena's return, Sundowns' defensive vulnerabilities remain a concern. They will need greater solidity when they attempt to overturn a 1-0 first-leg deficit against Golden Arrows in the MTN8 semi-final second leg on Sunday.
