United finally broke down Leicester's resilient rearguard and maintained their 100% start to the season through goals from substitutes Marcus Rashford and Marouane Fellaini.
Having won the first two matches against West Ham and Swansea with a 4-0 scoreline, the Reds passed the sternest test of their credentials so far and continue to set the Premier League pace.
We were made to work hard for the win, though, with Kasper Schmeichel in superb form as the champions from two seasons defended doggedly and in numbers for much of the contest.
The Reds had applied constant pressure on the Foxes massed defence and endured an afternoon of frustration as Schmeichel saved a Romelu Lukaku penalty in the second half.
That was until Rashford - three minutes after he had come on - fired in from Henrikh Mkhitaryan's corner to break the deadlock with 20 to play.
Fellow sub Fellaini then added a second from close range to put the result beyond doubt eight minutes from time.
United started strongly and thought they had gone ahead early on when Juan Mata pounced on the rebound of Lukaku's saved shot, only to be flagged offside.
The Reds bossed possession during the opening half, in no small part down to the Reds midfield dominance against Craig Shakespeare's Leicester side.
Despite the lack of a goal, it was not for the want of trying as Paul Pogba twice went close from distance and Schmeichel saved superbly from Mata.
Seven minutes into the second half United were quite literally handed the chance to go ahead when Danny Simpson was adjudged to have handled a Martial cross.
Lukaku stepped up to take the spot-kick but was denied his fourth goal of the season as Schmeichel guessed right and brilliantly pushed it away.
Having started those first two league games, Rashford was then introduced in place of Martial and the change reaped dividends for Jose and the team.
Mkhitaryan's flag-kick - his fifth assist of the campaign already - picked out the young striker and he volleyed in his first of the season from ten yards on 70 minutes.
From then on, the result never looked in doubt but Fellaini gave the hosts breathing space when he turned home fellow substitute Jesse Lingard's shot, despite suspicions of offside.
David de Gea had been a virtual spectator throughout, such was United's dominance, but the keeper was called into action at the death.
A superb point-blank stop from Andy King preserved the Reds third consecutive clean sheet and sent United into the international break sitting atop the Premier League summit.
Overall team performance: 8.5/10
United Faithful Man of the Match: Paul Pogba