It's the first time United have recorded three straight Premier League wins since April 2021 as they rediscover their momentum after a nightmare start.
Manchester United boss Erik ten Hag now has the chance to end Arsenal's 100 per cent record when they visit Old Trafford on Sunday.
Leicester, meanwhile, remain bottom and winless from their opening five games with growing concern over how to salvage the season already.
It has been disrupted by Wesley Fofana's move to Chelsea, the inability to shift squad players and financial restrictions which have limited their spending ability.
Aside from a brief spell after the restart the Foxes struggled again and United always had a hold of the game.
Boss Brendan Rodgers has not lost four straight league games for 10 years - when Swansea boss - but that became a reality after 23 minutes.
United had enjoyed a controlled opening without piling on consistent pressure but they quickly seized the initiative when Leicester lost their way.
It was initially a decent kick by Danny Ward but it was quickly returned to Bruno Fernandes by Diogo Dalot with Luke Thomas woefully out of position.
The United skipper had time to pick out Marcus Rashford and the striker then played a cute ball for Sancho to run onto, round Ward and net his second goal of the season.
It was slick by the visitors but underlined the defensive problems Leicester have struggled with this season, having only managed to keep a clean sheet against Sky Bet League Two side Stockport.
With Fofana having completed his protracted £70million move to Chelsea on Wednesday, Wilfred Ndidi was parachuted in at centre-back and the patchwork nature of the hosts' defence continued to give United encouragement.
Another chance for Sancho came and went after Kiernan Dewsbury-Hall's ill-advised piece of skill gifted United the ball nine minutes before the break.
Leicester were flat but Harvey Barnes did at least fire wide before the break with United holding a worrying degree of control as far as Rodgers was concerned.
It was United's best half of the season, although aided by the anaemic Foxes, but the hosts emerged after the restart with renewed vigour.
David De Gea needed to turn James Maddison's free-kick away, after Dewsbury-Hall broke when Fernandes casually lost possession, which lifted the King Power Stadium.
It was the first time the visitors were under pressure and Ten Hag reacted by replacing Anthony Elanga with Casemiro just before the hour.
The £70million midfielder immediately brought an air of composure, one United needed, and Leicester's threat waned.
United had failed to create anything to increase their lead but seemed happy to hold on to what they had.
It was only when Cristiano Ronaldo was given a cameo off the bench that they came close and he teed up Rashford to slice wastefully wide with nine minutes left.
An ambitious scissor kick from Ronaldo dropped wide two minutes later and Kelechi Iheanacho diverted Fernandes' cross over his own bar.
But United claimed the points, escaping a late scare when James Justin blazed over in stoppage time.