The Foxes took a 29th-minute lead through Welsh forward Chris Popov, who shifted Joe Wormleighton's pass from his right foot to left before finishing past Radek Vitek.
United grew into the game after a slow start and excelled in the latter stages of the first half. Dan Gore's impressive footwork drew a foul on the edge of Leicester's penalty area and Garnacho scored from the resulting free-kick, directing a curling shot into the bottom left corner.
A frenetic start to the second half followed. Charlie McNeill worked a chance with a one-two with Garnacho and saw Arlo Doherty make an excellent left-handed save.