Jon Daly netted from the penalty spot 10 minutes into the second half at Tannadice, after Liam Kelly was dismissed for a last-man challenge on Gary Mackay-Steven.
Paul Dixon blasted a superb 30-yard effort to double the hosts' lead and John Rankin then slammed home their third with 20 minutes remaining.
With six minutes left Scott Robertson capped an excellent display by firing beyond Bell to add gloss to a superb evening for the Tannadice side.
"It's good to take all three points and put in a good performance too," said Houston, whose side drew 0-0 with St Mirren at the weekend.
"After Saturday's poor performance on the ball, I thought the lads were excellent tonight.
"We scored some cracking goals, we asked the guys to shoot and try to be less intricate and going on the second-half display we didn't have to ask twice.
"I am really pleased for John Rankin. It would have been a disappointment having been let go by Hibernian, but he has responded with a number of excellent performances - it wouldn't be a surprise to see him receive a number of the supporters awards at the end of the season."
Killie boss Kenny Shiels conceded his side were second best, but also expressed his disappointment at the display of referee Craig Thomson.
"It was a poor performance, there were contributing factors but they were the better team," he said.
"I was disappointed in Craig tonight, I thought he was off the pace, as we were. He struggled to keep up with play and handed out cards like confetti.
"That isn't why we were beaten though, we were beaten because the best team on the night won the game.
"We are going to try and correct our frailties after tonight and the referee maybe needs to look at his performance and try improve too."
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