Question marks were raised when it was revealed Zlatan Ibrahimovic would be starting from the bench but Marcus Rashford's early goal quickly distinguished United fans' fears.
It is now 22 Premier League games unbeaten for Jose Mourinho's side – a stat that has been readily ridiculed in recent weeks considering United's current position outside of the top four.
Jose Mourinho's side are now 22 Premier League games unbeaten
Manchester United became only the third team to keep a keep clean sheet against Chelsea this year
But former Chelsea star Nevin believes it is a record not to be sniffed at.
"I have to say I was surprised by how shocked people seemed to be by the result on Sunday at Old Trafford," Nevin told Chelsea's official website.
"It is worth getting it straight, Man United are on a monumentally good run without defeat.
Man United arrive for training looking glum despite Chelsea win Tue, April 18, 2017
Manchester United manager Jose Mourinho and his player looked less-than-impressed as they arrived for training on Tuesday morning, despite their win over Chelsea at the weekend
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Manchester United arrive for training ahead of their clash with Anderlecht
"For all that they draw too many games, they have the biggest squad in terms of quality in the league and they were playing at home.
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"They had everything to play for in that they are striving for that Champions League place, which I have always felt they will get, and have a manager who is quite good technically and tactically!
"Actually he is better than quite good at the tactical side as we know more than anyone, but his inside knowledge of the Chelsea team was the killer on the day.
"He knew where to strangle our creativity and he managed to fire up his own players.
"On top of that they got lucky with both goals for different reasons (if the referee has missed Herrera’s hand ball in the build-up to the opening goal, the officials helping him surely must have seen it) and our lads had something of an off day as a group, not helped by Thibaut Courtois and Marcos Alonso being unavailable.
"In short, it was a perfect storm with so much to contend with and who said it was going to be easy anyway?"