After a tense first 45 minutes, two second half United goals, courtesy of Bruno Fernandes and Jesse Lingard, were enough to beat a Leicester side who were reduced to 10 men after a late Jonny Evans red card.
Story of the match
Nervy opening 45 minutes
In what was arguably the biggest game of the closing day, the first half displayed a very cagey affair as neither side wanted to give the opposition the advantage.
Both sides enjoyed attacking football but it was the lack of accuracy that let down the likes of Mason Greenwood, Kelechi Iheanacho, Anthony Martial and Youri Tielemans, all of whom saw shots in promising positions fail to hit the mark.
It was the visitors who finished the second half slightly the stronger of the two sides, with Marcus Rashford stinging the palms of Kasper Schmeichel with a venomous shot before the half time whistle, but Brendan Rodgers would have been the happier of the two managers.
Penalties proving prosperous for United once again
With Chelsea firing two goals in quick succession in their match against Wolverhampton Wanderers before half-time, the picture looked different for Leicester, who now had to win the game in order to achieve a top four place.
The Foxes were looking like they were growing into the game, with Jamie Vardy hitting the corner of the crossbar and the post with a looping, glancing header but it was the home side who allowed United to land the first major blow.
Hamza Choudhury held onto the ball for too long in his own third and a pressing United swiftly won the ball and played through Martial, who was brought down in the box by a combination of Jonny Evans and Wes Morgan to win their 20th penalty of the season. A tired looking Fernandes placed the ball on the sport and converted clinically to put his side in the driving seat with 71 minutes played.
The pressure of chasing the game, and ultimately their season seemingly took the toll on Leicester. Harvey Barnes came the closest to equalising after swivelling to shoot in the box, only for David de Gea to catch the shot comfortably, before a swinging Wes Morgan boot failed to connect with a Luke Thomas cross in a promising position.
Leicester became more reckless as their time was running out, proving to be their downfall. A stretching Jonny Evans connected with the ankles of Scott McTominay rather than the ball, earning him a straight red card in the 94th minute, reducing the chasing home side to 10 men.
In the dying embers of the game, Schmeichel, like Choudhury, held onto the ball for too long in his own box, only to be dispossessed by Jesse Lingard to slot home his first goal of the season with practically the final kick of the season.
Due to this, it was United who claimed the Champions League and Leicester, who were 15 points clear of The Red Devils at one stage of the season, have to settle for a spot in the Europa League.
Lack of form and unfortunate injuries cost Leicester top four
Leicester enjoyed a lightning start to the season and cemented their place in the top three and looked like they were guaranteed a Champions League place.
The second half of the season saw them lose to the likes of Norwich and a Southampton side that they had scored nine goals past as a blip in form turned into a pattern.
Coupled with the injuries to key players Ricardo Pereira, James Maddison, Ben Chilwell and a suspension to Caglar Soyuncu meant Leicester had to constantly change personnel and formation in order to adapt, something that they struggled to do as they limped over the Premier League finishing line having squandered such a big lead.
Man Utd showed more experience
A club of the size and stature of Man Utd have plenty of experience in securing top four places and seeing out matches and that experience proved to be the difference.
The away side defended astutely against an inexperienced Leicester side and made them pay for their rashness, with both goals coming from Leicester mistakes at the back.
After establishing the lead, tactical fouls, well timed substitutions and hold-up play from their strikers effectively ran down the clock and in turn, led Leicester to self implode with the Evans dismissal and the gift of the final goal by Schmeichel.
Leicester have a big summer ahead
With the ongoing pandemic and the losing of Champions League football, Leicester's summer will go a long way in showing where the Foxes will go as a club going forward.
Key players such as Maddison, Chilwell, Barnes and Soyuncu have been linked with moves away from the King Power Stadium and the lack of Champions League could make it more difficult for the East Midlands side to keep hold of their assets.
Likewise, recruitment will also be key, as proven by the reliance of Vardy in attack, the lack of goals around the team and the depth in defence, something that will need to be addressed with a long campaign in Europe ahead.