But the Premier League champions, who hit the crossbar through Shinzi Okazaki, hit back after the break when Jamie Vardy pounced on an error from Marouane Fellaini to equalise.
United, who also handed a debut to defender Eric Bailly, spurned a chance through Zlatan while Foxes new signing Ahmed Musa was guilty of a bad miss in the closing stages.
But it was Zlatan who had the final say with a header, although replays showed he was just off-side, to give Mourinho his first trophy.
Zlatan Ibrahimovic, Manchester United celebration, AFP
Image credit: AFP
And it was a good day all round for the FA Cup holders with the news today that Paul Pogba is set to have a medical ahead of his world record move.
How did Zlatan fare on his competitive debut? By his lofty standards he was very quiet playing in a deep role until the 83rd minute. The Swede had one chance to score which he fluffed from close range and his link-up play with Anthony Martial and a below-par Wayne Rooney was patchy. He had to use his physical strength to deal with Leicester's defenders but eventually delivered with a brilliant trademark header to steal the headlines.
Manchester United's Jesse Lingard scores their first goal - Leicester City v Manchester United - FA Community Shield - Wembley Stadium - 7/8/16
Image credit: Reuters
MAN OF THE MATCH
Eric Bailly (Manchester United): After a nervy start, the Ivorian showed his strength and speed with a series of important challenges and clearances. He was booked for one too many barges but looked solid for a 22-year-old playing his first game in English football.