Juan Mata was on song for Manchester United as he scored the only goal of the match, keeping the team intact in their UEFA Champions League aspirations.
But for their hosts, it was a gloomy day going 0-1 down as the loss slipped them closer towards Barclays Premier League relegation.
Mata netted the decisive goal in the 72nd minute, meeting Wayne Rooney’s layoff with a composed strike beyond John Ruddy.
United started four points adrift of Manchester City in the race for the top four and, with Louis van Gaal leaving out Marcus Rashford and Daley Blind, were dealt a blow in the warm-up, when Anthony Martial suffered an injury and was replaced by Ander Herrera.
Matteo Darmian also had to make way due to injury in the opening stages and United’s struggled to make an impact in the final third for much of the match.
Norwich failed to threaten finding an equaliser and remain two points adrift of safety with Newcastle United and Sunderland facing Aston Villa and Chelsea respectively later in the day.