The Spanish striker met a Cesar Azpilicueta cross in the 55th minute with a powerful header that looped over David de Gea and won the game for Chelsea with his eighth goal of the season.
United began the game brilliantly and came close to scoring through Marcus Rashford's looping header in the first 20 minutes. However, they faded badly and posed little threat during a desperately poor second-half display.
Full-time: Chelsea 1-0 Man Utd @AlvaroMorata's brilliant header secures the three points for the Blues!November 5, 2017
The defeat means they are now eight points behind Premier League leaders Manchester City, whose seemingly unstoppable march at the summit continued with a comprehensive 3-1 win over Arsenal earlier on Sunday.
Chelsea, who have now lost just once to United at Stamford Bridge in 16 league games, remain in fourth place, but are just a point behind their beaten opponents and Tottenham.