First half goals from Wayne Rooney and Patrice Evra came either side of Fraizer Campbell's equaliser for the hosts, who tested the champions throughout but rarely threatened goalkeeper David De Gea prior to Kim's late leveller.
United might still have pinched the points in injury-time when Rooney was played in on goal, but the striker scuffed his attempted pass to substitute Danny Welbeck and City stopper David Marshall pounced on the loose ball.
Shorn of several key players through injury, including top scorer Robin van Persie, manager David Moyes made five changes to the side which overcame Arsenal prior to the recent international hiatus, and that sizeable reshuffle contributed to a disjointed first half display from the champions.
Rooney provided the majority of the game's talking points, kicking out at Jordon Mutch early on after the City midfielder had blocked the striker's forward surge. Referee Neil Swarbrick brandished a yellow card, to Cardiff's ire, and the home contingent's sense of injustice was heightened when Rooney soon opened the scoring.
Antonio Valencia and Chicharito combined to tee up United's no.10, who took his time before unleashing a near-post effort which nicked Gary Medel and looped over the stranded David Marshall. Though the City goalkeeper was soon required to fend away a Marouane Fellaini header, it was the hosts who took the initiative for the remainder of the half.