Kilmarnock's festive hangover continued as goals from a player who has plagued them for a decade and a former favourite condemned them to a third consecutive defeat.
United took a deserved lead in the 21st minute and, in keeping with a poor game, it was a soft goal to concede.
Mark Wilson swung in a regulation free-kick from the right touchline which Gordon Greer rose to clear. However, the big central defender mistimed his leap and the ball sailed over his head straight to Billy Dodds who had the simple task of hammering the ball low past the stranded Francois Dubourdeau.
Kilmarnock had a strong penalty claim turned down in the 29th minute when Gary McDonald's header was stopped by David McCracken's hand, but referee Kevin Toner judged that it was accidental and allowed the defence to clear.
United continued to enjoy the lion's share of possession in the first half and could have gone two ahead when Jim McIntyre toyed with Freddy Dindeleux before delivering a deep cross to Barry Robson, bit the midfielder could only blast his shot over the bar.
Killie showed more fight at the start of the second half and almost grabbed an equaliser on the hour mark when Colin Nish rose to meet Steve Fulton's free-kick only for his header to rebound back off the post.
Killie introduced Kris Boyd to provide some much-needed aggression and they began to ask more questions although they still could not force United keeper Paul Gallacher into any serious action.
The visitors sealed their victory ten minutes from time with a hotly-disputed penalty.
Substitute Jason Scotland burst into the box and was brought down by Fulton who appeared to win the ball cleanly. However, Mr Toner awarded the spot-kick which McIntyre, a Killie cup winner in 1997, cheekily chipped into the roof of the net.