After a first half in which the Tangerines had held their own, their weak defence quite simply caved in as the Bhoys moved up a gear and deservedly won by such a convincing margin, scoring four goals in a blistering 15 minute period.
United had taken a shock lead with only five minutes on the clock following a blunder by Celtic keeper Artur Boruc.
Noel Hunt found space 20 yards and dispatched a shot which the Pole inexplicably mis-judged and seemed to dive over on its way into the net.
Not surprisingly the visitors upped the tempo with Jiri Jarosik heading over in the 11th minute from a great position six yards out.
Then five minutes later Shaun Maloney tormented David Proctor on the left before cutting in and firing a powerful drive narrowly wide.
United should have made it two but an incredible miss from Barry Robson prevented them from extending the lead. The captain completely miscued and an absolute sitter went begging.
One minute from the break the visitors grabbed the equaliser, although there was a hint of controversy attached to it.
Following a Gary Caldwell free-kick, Shunsuke Nakamura's shot flew into the air and when the ball came back to the Japan international courtesy of Jarosik's header he appeared to be offside as he prodded home from four yards.
Two minutes after the break the Hoops grabbed the lead with Nakamura on the mark again.
Jan Vennegoor of Hesselink flicked Lee Naylor's throw on to Nakamura who took advantage of slack marking to steer the ball home.
It was game over five minutes later when Hesselink added a third.
Nakamura slipped the ball through to Maloney who dinked it through to the Ducthman who in turn rounded Derek Stillie and slipped the ball home from an acute angle.
It was a brilliant goal in the 58th minute which had the visiting fans on there feet saluting a Nakamura hat-trick.
Excellent work by Jarosik on the left teed up the midfielder who picked his spot in the top corner from 12 yards to complete the fightback.