"We're winning ugly," Chiefs captain Sam Cane admitted as one of the leading sides in the competition struggled to hold off the worst performing team.
They were also denied a bonus point despite the Sunwolves having two players sent from the field in the penultimate move of the game.
With the resulting penalty, the Chiefs opted to ignore their two-man overlap and drove at the line only to be held up by the determined Japanese outfit.
For much of the game, the unfancied Sunwolves tore up the form book and were the dominant side as they humbled the Chiefs' forwards in the set pieces and floored the Waikato backs with crunching tackles.
But the outcome was settled when the Chiefs piled on 15 points to close out the first half.
The Sunwolves, from being a slender 5-3 behind after the first quarter, found themselves trailing 20-3 at half-time.
They came back to win the second half 17-7 but could not completely close the gap.
"A tough night's a good way to put," Cane said. "The Sunwolves came to play. They're adventurous, they throw the ball around, and gee they play with some courage and they put us under pressure.
"But we got the win. We're winning ugly at the moment which is tough for us."
It was a bold effort by the Sunwolves whose maiden visit to New Zealand had seen them lose 50-3 to the Canterbury Crusaders and 40-15 to the Otago Highlanders.
Another high score seemed on the cards when Hika Elliot scored for the Chiefs in the third minute but the Sunwolves had other ideas.
They controlled the next 20 minutes, during which they won four penalties inside the Chiefs' 22, although referee Will Houston did not find this excessive and there was no warning issued.
After battering away at the line for no reward, the Sunwolves took the points with a fifth penalty which fly-half Hayden Cripps converted.
Relief for the Chiefs came when McKenzie combined with Aaron Cruden to send Solomon Alaimalo over for a try.
He added a penalty and then beat three defenders to score and convert himself as the Chiefs pulled away to a 20-3 lead at the break.
A revived Sunwolves took control at the start of the second half and were rewarded with a try to Fumiaki Tanaka.
When McKenzie added his second try for the Chiefs, Derek Carpenter responded with a second for the Sunwolves which was converted by Jamie-Jerry Taulagi who also landed a penalty.
With time up and the Chiefs pressing for a bonus point try, the Sunwolves had Carpenter sin-binned for a deliberate knock down and Taulagi was red-carded for a shoulder charge.