The Swede found the winner late in the game after an opener from Jesse Lingard was cancelled out by Jamie Vardy.
Manchester United had much of the early play but it was Leicester City who looked more threatening when they got a sight of goal.
Content to absorb pressure and hit their opponents on the break, the Foxes had a great chance in the 19th minute as Vardy fed Shinji Okazaki who forced David De Gea to tip the ball around the post.
The resultant corner presented the Japan international with a second opportunity in quick succession and this time he slammed his header into the crossbar.
After that let off for United they broke the deadlock in the 32nd minute courtesy of a moment of individual brilliance from the scorer of the final goal of the Louis van Gaal era - Lingard.
The young Red Devil picked up the ball some distance out from goal and charged down field, evading the attentions of all ahead of him before easing the ball past Kasper Schmeichel whose touch was not enough to keep it out.
After the halftime break Leicester emerged with renewed vigour and it was rewarded in the 52nd minute when Marouane Fellaini gifted the opposition a goal.
With Vardy making tracks towards goal the Belgian nicked the ball off his feet before an under hit backpass was pounced upon by Vardy who rounded De Gea to score.
As the game entered its final ten minutes the sides needed a big character to step up to the plate and it was Manchester United's marquee signing Ibrahimovic who answered the call.