Manchester United confirmed their place in the top four with a 2-0 win at Leicester City, meaning Ole Gunnar Solskjaer's side finish third in the Premier League.
In a final-day shootout with Brendan Rodgers' side at the King Power Stadium, where the winners would guarantee Champions League football next season, nerves were on show until Bruno Fernandes settled the visitors down from the penalty spot (71) after Anthony Martial was taken down by Jonny Evans and Wes Morgan.
The penalty was United's 20th of the season and their 14th in the Premier League - a new record.
Evans was shown a red card in injury-time for a dangerous tackle on Scott McTominay before Jesse Lingard broke his duck for the season (90+6) with the final kick of the game, taking advantage of a terrible error from Kasper Schmeichel.
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Jamie Vardy, who won the Golden Boot with 23 goals, hit the woodwork for the hosts at 0-0 but ultimately their season fizzled out after taking just two points from the last 21 available.
Leicester had been in the top four for 298 days until dropping to fifth in midweek as a sharp decline in form since the resumption put paid to their Champions League dream. It is the Europa League for them.
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Leicester: Schmeichel (5), Morgan (6), Evans (5), Justin (7), Thomas (6), Ndidi (6), Tielemans (6), Choudhury (5), Albrighton (6), Vardy (6), Iheanacho (6)
Subs used: Gray (6), Barnes (6), Hirst (N/A)
Man Utd: De Gea (7), Wan-Bissaka (7), Lindelof (7), Maguire (7), Williams (7), Pogba (7), Matic (7), Greenwood (6), Fernandes (7), Rashford (6), Martial (8)
Subs used: Lingard (7), McTominay (6)
Man of the match: Anthony Martial
How United got the job done...
In a game full of tension from the outset, both teams looked leggy after a relentless period of games.
Mason Greenwood guided a header over for the visitors as he went searching for his 19th goal of the season as Leicester defended deep to try and quell the threat of United's pace in behind.
- Ole Gunnar Solskjaer selected Aaron Wan-Bissaka in place of Timothy Fosu-Mensah at full-back – that was the only change from the draw with West Ham.
- Brendan Rodgers made three changes from Leicester’s defeat at Tottenham and decided to play Kelechi Iheanacho up top in a two with Jamie Vardy
Kelechi Iheanacho was finding space for Leicester on the counter attack and he scuffed a good opportunity to test David de Gea, who still managed to spill a weak shot, but Vardy was offside so could not take advantage of the fumble.
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Youri Tielemans rolled a low effort wide before Marcus Rashford curled over after James Justin missed Paul Pogba's pass.
Justin was forced into an excellent tackle to halt Martial, whose movement in behind was United's most potent weapon.
Leicester were very much in the game, though, and knew a goal would completely turn the complexion of the situation around. Their chance came just after the hour when Vardy flicked Tielemans' free-kick onto the angle of post and bar.
It proved to be Leicester's best chance as, with Leicester pushing a little higher up the pitch, Martial eventually got in behind one too many times. A perfect ball from the otherwise quiet Fernandes found Martial and a combination of Evans and Morgan took the striker out.
Fernandes then rolled in his 10th goal of the season from the spot.
Leicester tried to stage a late fightback but the final finish was lacking as Morgan missed his kick when well placed and Demarai Gray firing wide from a tight angle.
With the game almost over, Lingard then rubbed salt into the wounds when he tackled a dallying Schmeichel and fired into an empty net.
United can celebrate just their third top-four finish in the seven Premier League seasons since Sir Alex Ferguson retired. Solskjaer has got United moving in the right direction.
Man United boss Ole Gunnar Solskjaer: "It's a massive achievement by the staff and players. They are incredible. I had a chat with all of them today saying no matter what happened today we'd had a fantastic season. We're building a culture. I'm very pleased and proud of their efforts. To win this game was massive mentally as we've lost two semi-finals."
Leicester boss Brendan Rodgers: "We finished in the second-highest league position in the club's Premier League history. It takes us into Europe and I'm really excited by that.
"It's that next step for this squad. We've arrived a bit earlier than what we thought but the boys have had a very good season. I can't fault their effort and spirit. Next year it's about ambition, improving the quality and this experience will serve us really well."
Sky Sports' Gary Neville:
"It's a big day for Ole. It will give him some peace. It demonstrates the progression we have seen in the last few months. The team are better, they are younger and they can play a different way now than they could at the start of the season.
"They were really basic in the sense they just played counter-attack [earlier in the season]. With Bruno Fernandes and Paul Pogba, and Mason Greenwood emerging, they look like they can play different ways and win different ways.
"But when you play the same team, that first eleven, for a week or two, they start to get fatigued. That demonstrates they need more players in the squad. The last time Manchester United finished in the top three was under Jose Mourinho and they spent £170m that summer.
"United need to invest money again but do it correctly this time. The squad needs improving, the team needs improving. First and foremost, they need to improve the first eleven."
Man of the match: Anthony Martial
United's joint-top scorer this season with 22 goals (17 Premier League) - the best scoring season of his career - was once again in fully motivated mood to make a difference for his team. It's this consistency within his game that has taken him to the next level this season. He's become an integral player in the way United attack, as shown by his clever movement throughout the 90 minutes against Evans and Morgan, who always looked petrified of getting turned by the Frenchman. It was his break in behind and the ability to draw the foul off Evans that was the game-changing moment.
What the managers said
Brendan Rodgers said: "Absolutely, we're excited by that [Europe]. We finished in the second-highest league position in the club's Premier League history. It takes us into Europe and I'm really excited by that.
"It's that next step for this squad. We've arrived a bit earlier than what we thought but the boys have had a very good season.
"I can't fault their effort and spirit. Next year it's about ambition, improving the quality and this experience will serve us really well."
Ole Gunnar Solskjaer said: "I believe in what I do and believe in what I've been doing. We all have different ideas of management and I do it my way. That's the only way I can do it. The players bought into it and have taken on board what we've been doing. I'm not going to say I'm not the man, of course, as I'm in the job. I believe in what I'm doing.
"It's a massive achievement by the staff and players. They are incredible. I had a chat with all of them today saying no matter what happened today we'd had a fantastic season. We're building a culture. I'm very pleased and proud of their efforts. To win this game was massive mentally as we've lost two semi-finals."
- Leicester manager Brendan Rodgers has lost 10 of his 12 meetings with Manchester United across all competitions (W2), suffering defeats in each of the last five.
- United extended their unbeaten run to 14 games in the Premier League (W9 D5); their longest run without defeat in the competition since April 2017 (25 games).
- Since making his debut in the competition in February, Fernandes has been directly involved in more goals in the competition than any other player (15 - eight goals and seven assists).
Manchester United still have a Europa League campaign to negotiate with their second-leg clash with LASK on Wednesday August 5.
The 2020/21 Premier League season kicks off on September 12, and will run until May 23. The EFL has confirmed the Championship season will commence on the same weekend, with their regular seasons ending on the weekend of May 8.
Premier League clubs have voted for the summer transfer window to open the day after the 2019/20 season ends - on Monday July 27 - and run for 10 weeks.