Marcus Rashford, who scored twice in a 4-2 victory over Arsenal at Old Trafford last month, scored in another big game for the Red Devils after the young striker broke the deadlock in the 16th minute.
The 18-year-old was denied a penalty on the stroke of half-time but Martin Demichelis and the City defence escaped unpunished.
City had 26 attempts on goal and Sergio Aguero missed a number of decent opportunities to bag an equaliser for the hosts at the Etihad Stadium.
Seemingly feeling buoyed after Arsenal’s 2-0 victory over Everton at Goodison Park on Saturday afternoon, Gunners supporters Morgan poked fun at the Manchester clubs, who are trailing Arsene Wenger’s side.
Who won the mid-table Manchester derby?
— Piers Morgan (@piersmorgan) March 20, 2016
United are in sixth place and a point behind fourth-placed City in the race to secure a place in next season’s Champions League competition.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news