All Blacks flanker Liam Messam celebrated his 150th match for the Chiefs, helping to secure a bonus point by killing off a late raid on the try-line by the Pretoria-based visitors.
The South Africans battled hard but were kept try-less at Waikato Stadium, with flyhalf Handre Pollard kicking their entire score in penalties.
A dour contest in benign conditions played out until the Chiefs sparked into life 10 minutes after the break courtesy of the enterprising Stevenson.
The winger stepped past opposing flyer Jamba Ulengo near the right touch-line and chased down his own grubber kick for his team's first try.
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Flyhalf Aaron Cruden converted from a tight angle, then slotted an easier penalty as the Chiefs added 10 points in a five-minute burst.
Cruden and Pollard traded penalties as the arm-wrestle continued but scrumhalf Tawera Kerr-Barlow blew the game open with an inspired piece of play that set up the Chiefs' second try to McKenzie in the 71st minute.
Receiving the ball in a quick transition from a scrum near the left corner, Kerr-Barlow swerved through heavy traffic to kick the ball in front of the posts and a charging McKenzie collected it a few metres from the line before diving over.
Moli wrapped up the win in style, grabbing a pass at full stretch near the try-line before barging through a wall of defenders to touch down two minutes from the final siren.
(Reporting by Ian Ransom in Melbourne; Editing by Sudipto Ganguly)
