Following on from their last-start win over St Mirren, Killie did the job over Hearts at Tynecastle Stadium thanks to second-half goals from David Silva and Aleksei Eremenko.
Portuguese midfielder Silva ran at the Hearts defence, before drifting to the right and smashing a low shot past Marian Kello for his second league goal of the season.
Six minutes later, Eremenko received a neat pass from William Gross from the left flank before slotting home for a second for the visiting side.
However, the day turned sour for Eremenko when he was involved in a nasty clash with Hearts striker David Templeton which ended in the Finland international motioning towards a headbutt on home captain Marius Zaliukas and receiving a red card from referee Steven McLean with just under 20 minutes remaining.
Even with an extra man, Jim Jefferies’ men were unable to hit back and he was left to rue their lack of creativity.
"I felt today, when we got to that area, that one ball that can hurt you wasn't good enough," he said.
Killie boss Mixu Paatelainen felt that perhaps Eremenko was unlucky to be sent off as there were other incidences in the match which did not even bring about a caution.
"I realise how difficult a job they (referess) have," the Finn said.
"(But) we get players sent off for lesser offences than our opponents.
"It's unbelievable. I'm so disappointed - our player getting sent off and nothing happening to them.
"I agree with TV evidence. If I'm right saying what I'm saying here, yes (we will appeal).
"I saw exactly what happened out there - I had a good view."