The Red Devils wanted to continue their convincing start to the Premier League season against Leicester. The Foxes had also got off to a decent start to the campaign, and they arrived at Old Trafford determined to fight.
But straight from the off, the hosts looked to put Leicester under pressure, with crosses from both sides trying to break down a solid defensive layout.
Shakespeare's men attempted to test David De Gea in the initial stages, but eventually United took the upper hand and began to pile on the chances at the other end.
Some superb build-up play allowed the ball to come to Romelu Lukaku at the edge of the box. After showing the strength to fight off Maguire, he went for goal but Schmeichel made a good save with the rebound falling to Juan Mata. The Spaniard put the ball in the back of the net, but the offside flag was up.
Moments later, a flurry of chances came United's way, with Pogba firing a volley across goal after Martial's cross found him at the back post. Mata then danced his way into space inside the box and attempted to curl the ball into the top far corner but was denied by a stretching save from Schmeichel.
Leicester allowed Paul Pogba to try his luck from distance, the Frenchman given acres of space to see his thunderbolt strike from 25 yards whistle inches wide of the top corner.
The midfielder's aim seemed to be a bit off as he then skied his effort when Martial picked him out at the top of the box, and only minutes later another effort from distance flashed wide of the base of Schmeichel's goal.
Mourinho's team continued to assert their dominance well into the second half, seeing all of the ball with Leicester defending deep. Lukaku went down inside the box with United supporters appealing for a penalty, but referee Michael Oliver waved away the calls. Mere seconds after those claims were dismissed, Simpson saw his handball inside the box penalised.
Lukaku stood over the ball to score his side's first goal of the afternoon from the spot, but Schmeichel had other plans, leaping the right way to save the striker's powerful low strike.
Following the missed penalty, Leicester enjoyed a brief spell of creating chances, Riyad Mahrez proving a threat and forcing De Gea into action for the first time all afternoon.
However, as the fixture entered a dangerous stage for the hosts, with Leicester patiently waiting to hit United on the counter-attack, Mourinho's team found the breakthrough. Rashford, who had barely been on the pitch three minutes, won his side a corner down the right. Mkhitaryan provided the cross and it was Rashford himself who tapped home from six yards.
The home side breathed a sigh of relief after breaking the deadlock, and Mourinho introduced Fellaini and Lingard to the game. The substitution once again paid off with both players involved in the second goal.
Lingard ran down the left flank before lifting his head, holding the ball to wait for back up. The youngster fired his effort into the six-yard box, where Fellaini arrived in a tight poisition to guide the ball into the net with his thigh.
With the game well into stoppage time and Manchester United closer to claiming all three points, Leicester were awarded their best chance of the evening. Gray drilled a low ball into the near post where King was waiting to tap it home but De Gea stuck out a leg to deny the Welshman.
Lukaku had one final chance to get on the scoresheet, but his shot was sent over the bar by Schmeichel. The keeper kept the scoreline from being higher, but in the end Manchester United managed to continue their 100 per cent start with three wins and three clean sheets.