City are the first team to win 14 consecutive matches within the same season, and have equalled the top-flight record of 14 wins in a row, set by Arsenal across two campaigns in 2002.
They went ahead on 43 minutes when a Kevin De Bruyne corner ricocheted for David Silva to score from close range.
United equalised in first-half stoppage time as Marcus Rashford capitalised on a defensive mix-up before Nicolas Otamendi's fourth goal of the season restored City's lead.
But to go 11 points clear at the top of the table City required a stunning late double save from Ederson, as Pep Guardiola's side ended United's 24-match unbeaten home run.
Man Utd: 13 Dec v AFC Bournemouth (H)
Man City: 13 Dec v Swansea City (A)