Johnny Russell netted a hat-trick at Rugby Park as United leapfrogged the Ayrshire side into seventh place in the Clydesdale Bank Premier League two days after Houston announced he would not sign a new contract at the end of the season.
United were in control for much of the game and recovered well from an 18th-minute goal against the run of play from Manuel Pascali, who headed a second deep into injury time.
Houston said: "We've got a fantastic bunch of players. One thing for sure, and I said this at the press conference the other day, their attitude and commitment is 100% spot-on.
"We have played well in a lot of games this season and haven't got the results we deserve. We have had to chase games from behind, and just dug in to try to get results. We just need a wee break here and there and I thought some luck was going to go against us at times but the players were magnificent throughout the team.
"We worked very hard and I think we played some great stuff. Kilmarnock always get plenty of praise for passing the ball but I thought United were passing the ball for fun and playing triangles around them in the middle of the park."
Kilmarnock manager Kenny Shiels had a surprising analysis of the game as his side struggled to get forward in numbers for much of the game.
Shiels said: "There was nothing in the game, we got ourselves in front and were controlling the flow of the game. We were nullifying them totally and then the ball breaks and Russell, I was thinking to myself at the time he was a bit absent, and he scores a really good execution to equalise.
"The second half we were very good and in control of the game, quite dominant. They got the break of the ball, our left-back goes to block the cross and it comes off his foot and goes over the first centre-half. Russell is free and it's 2-1.
"Then the shift goes to them but we still have good control of the game, trying to get back into it but we push our centre-half up to chase the game and they get a third. But I think a draw (would have been) a fair account of the game."
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