After a dominant United start, Leicester led after Riyad Mahrez broke away to set up Jamie Vardy to fire home his 50th Premier League goal.
Mata got United level at the break with a low shot and then put United ahead with a curling free-kick on the hour.
Leicester’s task got harder when substitute Daniel Amartey earned two yellow cards only 16 minutes after coming on.
Jesse Lingard and Marcus Rashford spurned great chances to make it 3-1 and were made to pay as Marc Albrighton’s brilliant cross was turned in at the far post by Maguire.
The draw leaves United 13 points behind leaders Manchester City while Leicester stay in eighth.
Leicester: 26 Dec v Watford (A)
Man Utd: 26 Dec v Burnley (H)