A Tommy Miller penalty and Kuqi's first put Town 2-0 up but United hit back before the interval. A tight second half seemed in prospect, but it was broken open by three more Town goals in the space of nine minutes.
United started brightly with both Jon Harley and Paul Shaw firing off target but Town hit back when Ian Westlake put Miller clear, but he stubbed his toe, allowing Paddy Kenny an easy save.
Ipswich went ahead on 22 minutes when Phil Jagielka's weak back-pass was seized on by Darren Bent who was brought down as he rounded Kenny. The United keeper stayed on the field, and was not even being booked, but Miller fired the penalty low past his left hand.
A minute later it was 2-0 as Fabian Wilnis' long ball forward was missed by Bent, Jagielka and Chris Morgan and bounced up perfectly for Kuqi to loop his header over Kenny.
Richard Naylor missed a good heading chance from a Kevin Horlock free-kick as Town continued to dominate, but the visitors began to fight back and got a goal back just before the break.
Andy Liddell, a danger all night, swung in a free-kick which Naylor could only head clear as far as Leigh Bromby and he coolly fired low beyond a helpless Lewis Price.
United again started well after the break, with Town looking nervy at the back and both Bromby and Shaw fired efforts narrowly wide of the target.
But Town finally broke United's resistance with a spell of three goals in nine minutes as Naylor headed home a Jim Magilton corner on 62 minutes and then two minutes later Kuqi raced clear to fire home after being freed by Bent's flick-on.
The goal of the game though came on 71 minutes when Bent and Miller worked a one-two on the edge of the United box, freeing Miller to cross low for Westlake to steam in and flick the ball past Kenny from close range.
Town took their foot off the gas after that and United had chances for a consolation goal as Liddell saw a fierce shot well held by Price, Harley fired over and sub Jack Lester glanced a header wide from a cross by fellow replacement Nick Montgomery.
It was all about Ipswich though, and on this form they stand an excellent chance of collecting one of the two automatic promotion places, as they and Wigan are the form sides at present.
Town also set a new club record by scoring in this game, making it 29 regular season League matches in succession in which they have found the net, breaking the mark set way back in 1953.