A late equalizer salvaged a point for the hosts after goals from Wayne Rooney and Patrice Evra had given the away side the advantage, with Fraizer Campbell also scoring.
After Wayne Rooney had petulantly kicked out at Cardiff midfielder Jordon Mutch eight minutes in - an offense referee Neil Swarbrick deemed worthy only of a yellow card - the England striker duly gave United a 15th-minute lead.
However, Fraizer Campbell, who struck the crossbar after halftime, levelled matters before David Moyes' men led again as Patrice Evra glanced home Rooney's 45th-minute corner.
But substitute Kim darted in front of the France fullback to produce a similar finish from Peter Whittingham's free kick in injury time - the midfielder's deliveries having caused United problems all afternoon.
|VIEW FROM CARDIFF
|By Wayne Veysey at the Cardiff City Stadium
"Cardiff's vociferous fans and crammed stadium played a part in a priceless point for the hosts against the champions in another match dominated by refereeing controversy.
"Wayne Rooney scored one and created another but was extremely fortunate not to be sent off in the eighth minute, when he lashed out recklessly at Jordan Mutch. But the pace of Fraizer Campbell caused real problems to United center back pair Jonny Evans and Rio Ferdinand, which will be of great concern to David Moyes, who was without injured pair Nemanja Vidic and Phil Jones."
Mutch was preferred in the Cardiff midfield to Aron Gunnarsson, with Campbell leading the line against his former club.
Robin van Persie's absence because of a groin injury meant Chicharito partnered Rooney in attack for United.
The latter had an effort blocked and Mutch saw his header saved before the two came together in the first half's early flashpoint.
And Rooney was then, somewhat inevitably, the beneficiary when an error from Cardiff defender Ben Turner resulted in the champions taking a 15th-minute lead.
Turner's loose pass was collected by a rampaging Antonio Valencia and the Ecuador winger's cross was touched on by Hernandez for Rooney to check back and find the net, via a deflection off Gary Medel.
Marouane Fellaini drew a superb save from David Marshall when he headed Adnan Januzaj’s 20th-minute free-kick toward goal, but the young playmaker then erred near his own area, leading to Peter Odemwingie lashing the ball over the crossbar.
And Cardiff equalized in the 33rd minute when Whittingham and Mutch combined in midfield and the latter released Campbell for a composed finish.
The striker, Don Cowie and Whittingham all fired over for the hosts as United labored in defense of set pieces, although they demonstrated no such problems attacking them when Evra glanced home Rooney’s left-wing corner on the stroke of the interval.
Rooney's dead-ball deliveries continued to torment Cardiff upon the resumption and Marshall was at full stretch to deny Fellaini before beating away a header from Chris Smalling.
Malky Mackay's team responded once more and Campbell sent an audacious lob against De Gea's crossbar after Tom Cleverley had given away possession, with the rebound narrowly evading Mutch.
United might have earned some breathing space when Rooney headed Valencia’s 59th-minute cross over, while Whittingham sent a first-time effort just wide from distance six minutes later and Cleverley almost diverted a free kick from the same player into his own net.
Danny Welbeck thrashed wastefully beyond the crossbar 10 minutes from time and the United substitute was made to rue his profligacy when Kim stole in to snatch a share of the spoils, as Cardiff edged three points clear of the relegation zone.
Rooney could still have won it when he latched on to a ball over the top but his touch was poor - and Moyes was left to rue yet more dropped points.