Rodgers had questioned the mindset of his squad after defeat last Sunday meant there was no home title party this weekend.
With four changes for the home side, two up top and two at the back, the intent and desire was there instantly. Celtic were magnificent and swatted Kilmarnock away with some excellent goals.
The first was an individual moment of brilliance as Hatate gathered off a one-two and, without hesitation, fired straight into the top corner with Kieran O'Hara given no hope in goal.
Things quickly imploded for the visitors. Arne Engels waited and waited before playing a delightful ball in behind for Alistair Johnston, who squared for Maeda to tap in the easiest of his now 31 goals this season.
Celtic's attacking was relentless and Carter-Vickers got in on the act as he strode freely towards the box and smashed a perfect long-range strike into the top corner.
The fourth was wonderfully worked with James Forrest again releasing Johnston, who found Hatate with space and time to net his second of the game and 10th of the season.
At that stage, Kilmarnock looked in freefall. From nowhere, Armstrong crossed with pace and it soared to the far post and over Viljami Sinisalo into the top corner. Fortunate but gratefully received.
Celtic kept at it. Kilmarnock avoided further damage just before half-time when Maeda slammed home but Adam Idah was adjudged just offside.
The only solace for the visitors was it didn't get much worse as they changed approach at the break to some effect. The damage was done.
Engels was closest to a fifth with a curling effort that clipped the bar before Ralston's late strike as Celtic inflicted a painful, chastening afternoon on their opponents.