The Chiefs scored two tries while Moana Pasifika were reduced to 13 men and went on to win 43-7 to stay on course for a home playoff in Super Rugby Pacific.
Scoring seven tries in all, the Chiefs took a bonus point and moved from fourth to third place at the start of the weekend's 12th round.
Tries on either side of halftime when Moana Pasifika had lost Irie Papuni and Aisea Halo to the sin-bin set up the Chiefs for their eighth win of the season, ensuring they will stay inside the top four for another week.
The first try and first points of the match didn't come until the 23rd minute. But after leading 12-0 at halftime, the Chiefs added three tries in the third quarter to lead 31-0 and five in a dominant second half.
After the Chiefs began to use the ball more effectively in the second quarter, flyhalf Josh Jacomb scored his first try in Super Rugby Pacific and centre Quinn Tupaea scored his first in two years as the Chiefs built their halftime lead.
Jacomb's try came on the blindside of a five meter scrum which Moana Pasifika defended with 13 men.
Papuni went to the sin-bin in the 26th minute for a head clash with Chiefs prop Ollie Norris and Halo was shown a yellow card for a professional foul.
Fullback Etene Nanai-Seturo extended the Chiefs' lead with a solo try immediately after the second half restart.
He pointed to a gap in the Moana Pasifika defence, kicked the ball to that spot, won the race to the bounce and spun out of a tackle to score.
Tries followed to center Anton Lienert-Brown and to Parker as a reward for his major impact on the match.
Moana Pasifika scored a consolation try through Anzelo Tuitavuki in the 71st minute.
"It was probably a bit shaky at halftime. We were just expecting things to happen," Chiefs captain Luke Jacobson said.
"Once we got into some good work, sorted our carry and clean, things clicked into place."
The win was an important one for the Chiefs who have a hard run home with matches to come against the first place Hurricanes and second place Blues.
Moana Pasifika's playoff hopes likely are now gone as they have to play the Wellington-based Hurricanes next week.