Fulham and Cardiff City suffered relegation as Sunderland beat Manchester United on a dramatic day in the battle for Premier League survival, while Manchester City moved top with a win at Everton.
Cardiff will join Fulham in the Championship next season after going down 3-0 to
Newcastle at St James' Park.
Newcastle had lost their previous six Premier League matches but they started strongly and Shola Ameobi headed them in front on 18 minutes from Moussa Sissokho's cross to the back post.
The match situation did not stop some Newcastle fans from staging a walk-out in protest against Alan Pardew and Mike Ashley midway through the second half, but Newcastle held on to triumph as Loic Remy and Steven Taylor scored goals from close range in the final three minutes to add gloss to the scoreline.
City top
Manchester City took the opportunity to climb to the top of the table with a thrilling 3-2 win at Goodison Park which extinguished
Everton's hopes of finishing fourth.
Ross Barkley fired Everton in front with a spectacular curling strike after 11 minutes but Sergio Aguero drew City level on 22 minutes after being played in by Yaya Toure.
Edin Dzeko headed in James Milner's cross after 43 minutes and then put City 3-1 ahead early in the second half from Samir Nasri's cross.
Leighton Baines' delivery was nodded in by Romelu Lukaku with 25 minutes still to play to give Everton hope, but City held on to go above Liverpool on goal difference with a couple of home games to follow.
Aston Villa overcame
Hull 3-1 in a clash between two sides who started the weekend still in with a chance of going down, but following results elsewhere Villa are now all-but safe and Hull have a five-point cushion.
Villa's nerves were settled by a goal inside the opening minute as Gabriel Agbonlahor delivered a cross from the left and Marc Albrighton, after missing the ball with his initial attempt at a first-time shot, laid it off for Ashley Westwood to pick his spot in the bottom corner.
A cleverly-worked free-kick routine after 28 minutes led to Hull's equaliser as Tom Huddlestone played the set-piece quickly to Liam Rosenior and, as the ball was fizzed across the six-yard box, substitute Jordan Bowery could do nothing but turn it into his own net.
Andreas Weimann restored Villa's lead when he nodded in after a desperate scramble in the area, and he then made it 3-1 with a much more stylish goal as he glanced a header past Steve Harper from Bowery's inviting cross.
In the day's early game,
West Ham ended a run of four defeats with a 2-0 victory over
Tottenham to raise their points tally to 40 and guarantee their top-flight status for another season.
Sam Allardyce has grown frustrated by criticism from fans in recent times but the Upton Park faithful were celebrating after 25 minutes when Stewart Downing was pulled back outside the area by last man Younes Kaboul and the Spurs defender was shown a straight red card.
West Ham took the lead just a couple of minutes later when Andy Carroll's header took a crucial deflection off Harry Kane to loop over Hugo Lloris.
Downing added a second with a free-kick just before half-time which was driven straight through a disappointing defensive wall, and Spurs could not find a way back into the match with ten men as their hopes of European qualification suffered a blow.
Southampton edged out
Swansea 1-0 in an uninspiring contest at the Liberty Stadium.
The Swans had ensured their safety last week and there was an end-of-season feel to the match, but Southampton snatched all three points to make certain of finishing eighth when Rickie Lambert bundled the ball over the line in the 90th minute.
