Marcus Rashford gave United a great start, striking a swerving free-kick past Neil Etheridge after just three minutes.
United doubled their lead through Ander Herrera's deflected 25-metre shot.
Victor Camarasa pulled a goal back through a 38th-minute penalty after Rashford had handballed.
But Anthony Martial restored United's two-goal lead four minutes before the break after a wonderful passing move.
Jesse Lingard made it 4-1 from the spot on 57 minutes and got another in the last minute.
After scoring five goals in a Premier League fixture for the first time since Sir Alex Ferguson's final match in charge in May 2013, Man Utd are sixth on 29 points.
The defeat drops Cardiff down to 17th on 14 points.
Cardiff City: 26 Dec v Crystal Palace (A)
Man Utd: 26 Dec v Huddersfield (H)