Norwich City fans arrived for this match and immediately began taunting the few United fans who still sport anti-Glazer green-and-yellow neckwear with chants of "We've come for our scarves!" – and it quickly became clear that the visiting team were also on a mission.

They would have accomplished it if not for shoddy finishing, which was ultimately punished in typical fashion by United, who remain top of the Premier League but will surely have to play better than this to retain their title.

Sir Alex Ferguson made several changes to the team which, according to his programme notes, had been careless and lax during Wednesday's 3-3 Champions League draw with Basel, but the new personnel did not stimulate an improvement. In fact, United were lacklustre – and, in the continued absence of Nemanja Vidic and Chris Smalling, still defensively fragile. Jonny Evans, starting instead of Rio Ferdinand, was bullied by the Norwich striker Steve Morison. Anders Lindegaard, deployed in goal instead of David de Gea, sowed instability with some wayward kicks. Wayne Rooney and, especially, Javier Hernández were mostly shackled by the diligent visiting defence.

That pair's return from injury had looked ominous for the visitors – Rooney's nine League goals this season are two more than the entire Norwich team have managed – and although the England striker registered a shot on target within two minutes, Norwich generally kept him at arm's length.

Norwich should have scored in the fifth minute. Ferguson will surely have been angered by the ease with which Elliott Bennett got in behind Patrice Evra but perhaps not as angry as Morison was when the winger misdirected his cut-back, thwarting a tap-in. In the 17th minute, Morison created a chance for himself, chesting down a long ball from the back before shrugging Evans aside and firing wide from the edge of the area.

That, though, was as close as Norwich came in the first half as United gradually seized control. However, with Ashley Young given the weekend off and Nani subdued, the hosts lacked creativity, partially because of the discipline and tenacity of Norwich. Kyle Naughton exemplified that when he blocked a close-range shot from Hernández after a pass from Rooney, and Russell Martin did likewise when he nicked the ball off Nani in the box with a perfectly timed tackle.

United's best chances of the first period came from corners. Darren Fletcher met one of Nani's deliveries in the 33rd minute but his flick was cleared off the line by Marc Tierney.

Two minutes later Rooney challenged Martin for another Nani corner and the ball flew just over.

Although Norwich incursions into United territory became rarer, Morison remained a menace. He proved that in the 50th minute by receiving the ball on halfway, barging past Evans again and dashing into the box. Only a timely intervention from Jones prevented the striker from doing further damage.

It was a tribute to Norwich's defence that Ferguson withdrew Nani and Hernández on 65 minutes, introducing Danny Welbeck and Ryan Giggs instead.

Within seconds of that change Norwich should have taken the lead. Antonio Valencia dithered on the ball at the back and was dispossessed by Anthony Pilkington but, with only Lindegaard to beat, the midfielder steered his shot wide.

The cost of the miss soon soared as within two minutes Anderson finally broke through. Again a corner was the source of Norwich's problems. Giggs's delivery was headed on by Jones to Rooney and then to Anderson, who nodded in from close range.

The relief around Old Trafford was palpable. But Norwich were to inflict more frights. Anderson almost unwittingly helped their cause in the 76th minute when his deflection of a Pilkington shot wrongfooted Lindegaard. The ball bounced out off the post.

Norwich could have equalised in the 85th minute but, after they again prised United apart, Morison finished feebly.

Again United made the visitors pay for their profligacy. They swept downfield and Park Ji-sung teed up Welbeck for a tap-in.

"I'm gutted for the players," said the Norwich manager, Paul Lambert. "We played ever so well but if you create chances here you have to take them. But for a team that were in League One two years ago, we've performed really well."

Keep playing like this and it will be a very long time before they return to the lower leagues.