Ange Postecoglou hailed his Celtic side for producing some of their best football during a rampant opening spell at Rugby Park.
Celtic were four ahead inside 27 minutes thanks to a double from Matt O’Riley and goals from Kyogo Furuhashi and Daizen Maeda.
Kyogo also missed a penalty in that period to leave him one goal off the 30 mark for the season.
The Australian brought Yuki Kobayashi, Tomoki Iwata and Sead Haksabanovic into his team following the previous weekend’s victory over Rangers and they continued to sprint towards the Premiership title.
The 4-1 win left them 12 points and 29 goals clear of their Glasgow rivals with six games remaining.
He said: “First half the boys were outstanding. It was good as football we have played all year with the way we moved the ball and ourselves around the pitch.
“After last week’s big win you’re looking at where the focus is but it was important we started with a good intent and they did that.
“Second half got a bit sloppy and disjointed, the game in general, and we had to defend a bit more. But considering the challenge that was there, the boys handled it well.
“The guys coming in helped. When you are putting guys into a team that is already doing well, they have got motivation. There is certainly no complacency in them, they want to perform well and it gives everyone a lift.”
Postecoglou was delighted to see there was no let-up as his side bid to complete the task of retaining the title in style.
“It is important because, in a perfect world, you design your team to play its best football at the most important part,” he said.
“That’s not discounting the fact that you’ve got to be in this position to start with, so we’ve had to be pretty strong all year.
“But this is the time of year when things get decided and you want to be playing your best football. I thought the attitude was first-rate, it’s not an easy pitch to play on and a difficult opponent who are desperate for points.
“You can come here and try to get three points and move on but we came with an intent to play our football.”
Killie stemmed the tide – and netted a consolation through Liam Donnelly – thanks to a 31st-minute double substitution which saw defender Jeriel Dorsett and midfield enforcer Alan Power replace striker Christian Doidge and wide midfielder Fraser Murray.
Murray had a day to forget, gifting Furuhashi the opener with a slack backward pass, being beaten by Alistair Johnston as the Canadian set up Maeda, and then sending a clearance back the way of O’Riley who made it four.
Killie manager Derek McInnes likened watching the opening spell to a car crash.
“The first goal was such a sloppy goal,” he said. “It was a chance to be positive and the ball should have been in their box. The decision that was made to be negative in that situation, and it’s not what we wanted.
“It was a 20-minute period of a car crash just watching it unfold.
“I don’t like making early changes for obvious reasons, I want to support my team, but Doidge came off because we needed an extra midfielder and Fraser was really struggling after his mistake.
“I want players to show personality and courage to back themselves more. Sometimes when you lose a goal like that your eagerness to make up for it means you start jumping out the slots and thinking that’s the best answer.
“But it actually makes it worse and Celtic played in between us. That 20-minute period was so difficult for everybody to watch.
“The changes helped us clearly, we got a goal before half-time. The extra midfielder helped us and I thought we were the better team in second half. It was the team I wanted to see from the start.”