The champions had seen their lead cut to three points after Liverpool, who still have a game in hand, defeated West Ham United 1-0 at Anfield on Saturday.
A frenetic game saw United give City plenty to think about in the first half, although Pep Guardiola's side went into the break with a 2-1 lead.
City asserted complete control in the second period as was emphasised by the final scoreline.
Kevin De Bruyne gave the hosts the lead as early as the fifth minute after latching onto Bernardo Silva's cross but a brilliant Jadon Sancho effort levelled matters after 22 minutes.
De Bruyne ensured City went into the break ahead when he benefitted from a loose ball in the box and smashed beyond David De Gea in the United goal on 28 minutes.
Back from recess, United barely had a sniff of the ball but City had to wait until the 68th minute before extending their lead.
De Bruyne found Riyad Mahrez with a corner in the United penalty box and the Algerian's well-cushioned half-volley beat De Gea once again.
Mahrez completed his brace in stoppage time after smashing past De Gea from an Ilkay Gundogan through ball, with VAR needing to intervene to overrule the linesman's initial call for offside.
Man United now face a fight to secure a top four position, having dropped to fifth on the table and fourth-placed Arsenal having three games in hand.
