Killie captain Manuel Pascali opened and rounded off the scoring when he converted from corners but United dominated the vast majority of the game to vindicate Houston's assertion that there would be no ill effects from the announcement of his summer departure.
Thursday's news ended months of uncertainty over Houston's future but that was soon replaced by reports over who might replace him at the end of the season.
That will not derail Houston from his bid to secure his fourth top-half finish in the Clydesdale Bank Premier League in his fourth season as manager and United will give themselves a very good chance if they continue to play as they did at Rugby Park.
Their passing and movement was too much for Killie at times and Gary Mackay-Steven returned from a broken hand to add spark to their attacking play, while full-backs Barry Douglas and Keith Watson continue to improve and deliver numerous crosses into the box.
When asked about the speculation, Houston said: "I stopped reading papers and I don't read internet forums. I know what we are trying to do here and whoever it may be, good luck to them. I have made a decision and I want to fully focus on one thing and one thing only, and that's the remainder of the season.
"It would be great for me and the players, who have worked ever so hard, to get into the top six.
"Mackay-Steven has only played eight or nine games and he's a huge player for us. He sets the whole thing in motion sometimes going forward.
"When he's on his game I think we are a really good side.
"We have not had many breaks this season. The second part of the season usually comes good for us and this was a good start."