After thrashing Chelsea 4-0 on the opening day, United had failed to win any of their last three games but took all the points to inflict Leicester’s first defeat of the campaign.
Marcus Rashford scored the only goal from the penalty spot in the eighth minute after being tripped by Leicester defender Caglar Soyuncu.
Rashford could have got another in the second half, but his wonderful free-kick from 30 yards curled over the wall and onto the angle of crossbar and post.
Defender Harry Maguire, given a torrid reception by the Leicester supporters, came close to scoring against his old side but headed straight at Kasper Schmeichel.
Leicester grew into the contest with the lively James Maddison twice coming close and left-back Ben Chilwell saw his dipping effort tipped over by David de Gea.
The result means United leapfrog their opponents into fourth place, while Leicester drop down to fifth.
United came into the game on the back of 1-1 draws at Wolves and Southampton, as well as a home loss against Crystal Palace but boss Ole Gunnar Solskjaer had spoken beforehand about his side performing well without the positive results.
They managed to hold on to victory, which was just their second in their previous 10 league games.
England international Maguire became the world’s most expensive defender when he joined the Red Devils from Leicester for £80m in the summer and played his part as his side kept only their second clean sheet in the last 15.
Jeered by the travelling fans throughout, Maguire would have silenced those taunting him, but saw his towering header from a corner collected by Schmeichel.
