With Norwich 2-1 up but the game still in the balance, the United defence conspired to hand the visitors a gift of a goal to rubber-stamp the result.
For no apparent reason, Paddy Kenny came tearing off his line to challenge Darren Huckerby on the wing. Huckerby rode the challenge and played the ball across for Dean Ashton to shoot on the turn. His effort was curling wide until David Unsworth and Morgan tried to make sure, but after they got into a tangle the ball went in off the United captain.
It was a fitting way to settle an often scrappy game. Early on, Ashton failed to capitalise on a mistake in the United defence, firing wide from an unmarked position inside the area after good work from Paul McVeigh.
After an otherwise a slow start, United sparked into life in 19th minute.
First, Michael Tonge, handed only his seventh start of the season, tested Robert Green with a low fizzing shot from outside the area.
Moments later, Alan Quinn cut in from the right-wing, running onto Phil Jagielka's back-heeled pass, but his curling shot from inside the area bent just the wrong side of the post. They got their reward in the 22nd minute when Jagielka rose highest to head in Unsworth's corner.
They could have doubled the lead moments later when Neil Shipperley stabbed Danny Webber's cross back to Neil Montgomery, but he fired wide from the edge of the area.
Norwich then equalised against the run of play. Ashton's pass was headed on by Carl Robinson and McVeigh got in behind Unsworth to place a lot shot into the far corner. However, the Norwich forward was then booked for celebrating in front of the United fans - one of seven bookings in the game.
If the first half was scrappy, the start of the second half was even worse as both sides squandered possession and referee Trevor Kettle, who had blown for every incident in the before the break, now let most things go.
The first bright spot came in the 59th minute when Tonge sent a curling shot just wide after being released by Webber.
Norwich then stunned their hosts in the 62nd minute when Simon Charlton sent a long ball forward and Ashton beat the offside trap to beat Kenny with ease.
United look rattled, and McVeigh had a chance to score a third goal in the 66th minute, but fired over under pressure. Things descended into a real pantomime with Norwich's third goal in the 70th minute, and although United frantically sought a way back into the game late on, they were frustrated by Norwich's deep defending.