Tottenham signed out of White Hart Lane, and Hull left the Premier League.
Sunday's results meant there's only Champions League qualification at stake entering the final week of the season.
Tottenham locked down second place by beating Manchester United 2-1 in its final game before leaving its north London home of 118 years. Tottenham's hopes of catching newly crowned champion Chelsea ended a week ago, but it was still able to secure its highest finish in 54 years.
Tottenham's triumph ended Jose Mourinho's hopes of United making the top four, leaving three teams chasing the last two Champions League spots: Liverpool, which beat West Ham 4-0 on Sunday, Manchester City and Arsenal.
The three relegation spots have also been filled. Hull joined Sunderland and Middlesbrough in dropping into the second tier after losing 4-0 at Crystal Palace.
TOTTENHAM 2, MANCHESTER UNITED 1
Tottenham is leaving White Hart Lane after completing its best campaign at the stadium for more than a century. Spurs are due back on the site in a new 61,000-seat stadium in August 2018, after a season at Wembley.
This was the perfect send-off.
Victor Wanyama's sixth-minute header set the tone for a carnival atmosphere and Harry Kane added his 28th goal of the season at the start of the second half. United captain Wayne Rooney pulled one back but Tottenham held on to win before a ceremony, featuring past and current players, to bid farewell to the stadium.
The players are now looking to the future. By the time they are playing in the new home, they'll hope to have delivered Tottenham's first league title since 1961.
"It's been a progression from (third) last season," Kane said. "We've just got to keep it going, keep working hard, keep getting better and hopefully next season we'll finish first.
"To finish strong and finish unbeaten here is something special."
It wasn't so memorable for the "Special One," with Mourinho's hopes of qualifying for the Champions League with United now resting on beating Ajax in the Europa League final later this month.
"We know that it is a big objective, we know that if we lose the final we don't play Champions League," said Mourinho, who has already collected the League Cup. "But we fight for titles and probably other clubs finishing in the top four, probably they would like to be in our position to try to fight for a title."
WEST HAM 0, LIVERPOOL 4
Philippe Coutinho set up Daniel Sturridge before adding a superb double of his own. Divock Origi completed the rout with a tap-in as Liverpool ensured it will qualify for the Champions League, regardless of other results, by beating relegated Middlesbrough in next Sunday's season finale.
CRYSTAL PALACE 4, HULL 0
Crystal Palace manager Sam Allardyce maintained his status as a survival specialist, having never been relegated in management.
"I said to myself this would be the hardest one, given the quality of the teams we had to play on the run-in," Allardyce said. "If you've got the label, you accept it (as a firefighter), but building for the future relieves the stress on you. I wouldn't want to keep fighting relegation at the end of every season. It's about building for the future."
Marco Silva couldn't save Hull, though, in his five months in charge. Hull makes an instant return to the League Championship.
Hull never recovered after gifting Wilfried Zaha a third-minute goal. It was followed by Christian Benteke's header, Luka Milivojevic's 85th-minute penalty and Patrick van Aanholt's late strike.