United now find themselves 12 points behind Man City as Chelsea stay stuck in fifth.
Both teams created chances in an energetic start in the capital as Marcus Rashford’s free kick tested Edouard Mendy and Callum Hudson-Odoi flashed one wide.
And in a first half short on chances, it was VAR that caused the biggest talking point as Hudson-Odoi looked to get away with a handball in the United box.
And with the that slice of luck going their way before the break, Chelsea looked to up the ante after the restart, as Hakim Ziyech forced a smart stop from David De Gea.
But United were in no mood for rolling over late on Scott McTominay’s snapshot was beaten out by Mendy and Rashford was once again denied by the Senegalese star.
Both bosses made changes in the closing stages to inject some life into it but there was to be no way through at either end.
Full Time from Stamford Bridge it’s Chelsea 0 Manchester United 0
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