Five-eighths/fullback utility Damian McKenzie, who became the ninth player to reach the 1000 points mark in Super Rugby, said the side had been through the lows before getting on their high and knew they couldn't afford to get ahead of themselves.
He said it was about keeping their feet on the ground and getting better each week.
"It's never easy coming down here and playing against the Highlanders. Their backs are against the wall. That's when they're most dangerous, and they showed that at the start when they scored first.
"We found a lot of our attack came through counterattack and turnover ball, and we adapted pretty well to that and scored some great tries. We've got some guys in top form, which is great. We've just got to keep building.
"It was great to get a win for Alby's [Anton Lienert-Brown] 100th [club game] against the Highlanders who his brother plays for as well."
McKenzie said the counterattacking strength the side has displayed this year was largely instinctive.
There was a lot of their game built on structure and knowing where they were supposed to be.
"You only have to look at guys like Emoni [Narawa] and Shaun [Stevenson]. They like that stuff when we're in open space, and they have a free licence to do what they want.
"We do practice a little bit of that but some of it is instinct and those boys are playing some great footy so we just let them do their thing."
Highlanders coach Clarke Dermody thought they threw more at the Chiefs than they had in the previous few weeks, which was good, but also frustrating because they gifted them opportunities. This was through a combination of kick choice and turnovers.
"What we did wasn't wrong; it was just execution under pressure. Maybe a lift in intensity playing a Kiwi team again, and the consistency is not there yet.
He said that scoring tries against Kiwi teams had been a struggle for them, so scoring some against the Chiefs was good.
With injury problems in their middle row, flanker Shannon Frizell was forced into playing lock, and then Hugh Renton joined him for the last 10 minutes. Dermody was pleased with the problem-solving the side did under those circumstances.
Pressure on the locking stocks with Fabian Holland suffering a hamstring injury in the game, after having lost Pari Pari Parkinson, Will Tucker and Max Hicks before the game, and Josh Dickson cramping in his first game back after injury, is likely to result in a dispensation request to New Zealand Rugby for Shannon Frizell to play during his intended All Blacks rest week.
It would be a boost to have Frizell available.
"I thought he played well, mostly out of position but he got his hands on the ball a lot more which is what we have been asking of him. [He] looked into it and was defensively accurate and then around the goal line was dangerous with the ball in hand."