Newcastle's Champions League dream evaporated as Everton finished the season in style at Goodison Park.
Steven Pienaar opened the scoring from 20 yards with a shot which deflected off Newcastle defender Mike Williamson.
Nikica Jelavic doubled the lead at the second attempt after being denied by Tim Krul before Johnny Heitinga headed the third.
Pardew hails fantastic Newcastle effort
Everton, who had Tim Cahill sent off after the final whistle, were better despite Tony Hibbert's late own goal.
Substitute Cahill was dismissed after appearing to grab Yohan Cabaye by the neck.
Newcastle have enthralled and amazed in equal measures this season, but this was one game too many for Alan Pardew's side.
They deserve huge credit for staying in Champions League contention to the last game yet Newcastle end the season with three defeats in four games.
In contrast, Everton closed the campaign on the back of a nine-match unbeaten run in the league which allowed them to finish above Liverpool in the table for the first time since the 2004-05 campaign.
There were times during the game when David Moyes's side played as though it was their first, not last, match of the season, so delightful was their play.
They never looked back once Pienaar opened the scoring after 16 minutes with a 20-yard attempt, following Marouane Fellaini's run, which deflected off Mike Williamson.
Did you know?
Newcastle have lost 12 of their 14 Premier League visits to Merseyside
Pienaar, who is due to return to Tottenham after four months on loan at Goodison, was playing as though he had a point to prove.
The South African was denied a second goal by the foot of Newcastle keeper Tim Krul after Leon Osman had whipped the ball across the six-yard area.
Yet Everton were celebrating a deserved second goal after 27 minutes.
Jelavic was presented with the Premier League's Player of the Month award for April before the game and the Croatian demonstrated why he is one of the bargain buys of the season with another excellent finish.
The £5.5m signing from Rangers left Fabricio Coloccini trailing in his wake before Krul kept out his first attempt with a stunning save only for Jelavic to readjust himself and bury the ball in the back of the net.
Newcastle were a shadow of the side that had recently secured six straight Premier League wins.
Papiss Cisse went close on the stroke of half time while the Senegal striker was denied his 14th league goal since arriving from Freiburg in January when Tim Howard clawed away his effort.
Everton a match for anyone - David Moyes
Everton underlined their superiority when Heitinga made it 3-0 with a close range header following Darron Gibson's 65th minute cross.
Newcastle did find the net after Hibbert inadvertently headed past Howard following Ryan Taylor's long punt forward in the 73rd minute.
But the drama was far from over.
After Osman had hit the post in the dying moments, Cahill was shown a red card after the final whistle after raising his arm at Cabaye and had to be dragged away by his team-mates.
Everton manager David Moyes:
"I really don't know what happened (with Tim Cahill sending off). I felt the referee could have shown a wee bit of common sense.
"I really just wanted us to finish as high up the table as we possibly could.
"It didn't really bother me who we'd finish above, because I don't think you can really celebrate finishing seventh.
"The way I was brought up, you celebrate if you finish first or get Europe - if we'd finished seventh and got into Europe, that may have been something to shout about.
"But from where we were in October and November time, the teams we've had to overtake and the points we were behind, it's been a brilliant achievement by the players to come back from so far away."
Newcastle manager Alan Pardew:
"I can't fault my players. They have been absolutely brilliant this season and I don't think many of the top teams have won at Goodison Park this season.
"Arsenal and Tottenham both won so that softens the blow a little bit (of missing out on the Champions League).
Full Time The referee blows his whistle to end the game.
Foul by Marouane Fellaini on Jonas Gutierrez, free kick awarded. Direct free kick taken by Hatem Ben Arfa.
Shot by Leon Osman. Save made by Tim Krul.
Shot from inside the six-yard box by Leon Osman hits the post. Short corner taken by Steven Pienaar from the right by-line.
Inswinging corner taken from the left by-line by Darron Gibson.
Shola Ameobi gives away a free kick for an unfair challenge on Phil Jagielka. Phil Jagielka takes the free kick.
Darron Gibson takes a shot from a long way out which goes wide of the right-hand post.
Foul by Denis Stracqualursi on Mike Williamson, free kick awarded. Ryan Taylor takes the free kick.
Steven Pienaar fouled by Yohan Cabaye, the ref awards a free kick. Free kick taken by Sylvain Distin.
Darron Gibson gives away a free kick for an unfair challenge on Demba Ba. Ryan Taylor restarts play with the free kick.
Substitution Denis Stracqualursi on for Nikica Jelavic.
Darron Gibson takes a shot. Save by Tim Krul. Tim Cahill takes a shot. Save by Tim Krul.
Leighton Baines restarts play with the free kick.
Substitution Shola Ameobi replaces Cheick Tiote.
Unfair challenge on Nikica Jelavic by Cheick Tiote results in a free kick.
Marouane Fellaini takes a shot. Save by Tim Krul.
Papiss Cisse takes a shot. Tim Howard makes a save. Inswinging corner taken by Yohan Cabaye, clearance by Tim Cahill.
Handball by Nikica Jelavic. Direct free kick taken by Fabricio Coloccini.
Tony Hibbert fouled by Papiss Cisse, the ref awards a free kick. Phil Jagielka takes the direct free kick.
Marouane Fellaini is adjudged to have handled the ball. Free kick taken by Ryan Taylor.
Phil Jagielka restarts play with the free kick.
Substitution Tim Cahill comes on in place of Phil Neville.
Sylvain Distin fouled by Demba Ba, the ref awards a free kick.
Assist by Ryan Taylor.
72:01 Goal scored
Goal - Tony Hibbert - Everton 3 - 1 Newcastle Tony Hibbert heads into his own net. Everton 3-1 Newcastle.
Yohan Cabaye takes a shot. Save by Tim Howard. Corner taken by Ryan Taylor from the left by-line to the near post, clearance by Nikica Jelavic.
Tim Krul takes the free kick.
Substitution Sylvain Distin on for Johnny Heitinga.
The referee blows for offside against Marouane Fellaini.
Papiss Cisse is caught offside. Phil Jagielka restarts play with the free kick.
Darron Gibson provided the assist for the goal.
65:00 Goal scored
Goal - Johnny Heitinga - Everton 3 - 0 Newcastle Johnny Heitinga finds the back of the net with a headed goal from close range. Everton 3-0 Newcastle.
Unfair challenge on Nikica Jelavic by Fabricio Coloccini results in a free kick. Darron Gibson crosses the ball,
Demba Ba takes a shot. Johnny Heitinga gets a block in. Demba Ba takes a shot. Save made by Tim Howard.
Marouane Fellaini concedes a free kick for a foul on Yohan Cabaye. Direct free kick taken by Fabricio Coloccini.
Yohan Cabaye concedes a free kick for a foul on Steven Pienaar. Darron Gibson has a direct shot on goal from the free kick, save by Tim Krul.
Effort from 12 yards by Papiss Cisse.
Nikica Jelavic produces a left-footed shot from the edge of the box and misses to the left of the goal.
Ryan Taylor takes a shot. Johnny Heitinga gets a block in.
Johnny Heitinga challenges Demba Ba unfairly and gives away a free kick. The free kick is swung in right-footed by Ryan Taylor, Tim Howard makes a save.
Short corner taken by Ryan Taylor from the left by-line.
Leighton Baines gives away a free kick for an unfair challenge on Ryan Taylor. Ryan Taylor takes the direct free kick.
Hatem Ben Arfa has an effort at goal from outside the penalty box which goes wide right of the target.
Papiss Cisse has an effort at goal from just inside the box that misses to the left of the goal.
The referee gets the second half started.
Substitution Sylvain Marveaux comes on in place of James Perch.
Substitution Davide Santon leaves the field to be replaced by Ryan Taylor.
45:00 +3:54 Half time
Half Time The first half comes to an end.
Direct free kick taken by Yohan Cabaye.
45:00 +3:18 Booking
Booking Leighton Baines receives a caution for unsporting behaviour.
Free kick awarded for a foul by Leighton Baines on Jonas Gutierrez.
Free kick awarded for an unfair challenge on Jonas Gutierrez by Marouane Fellaini. Hatem Ben Arfa crosses the ball from the free kick left-footed from right wing.
Papiss Cisse produces a right-footed shot from just outside the box that goes wide right of the target.
Free kick awarded for an unfair challenge on Cheick Tiote by Leon Osman. Fabricio Coloccini takes the direct free kick.
Darron Gibson takes a shot. Save by Tim Krul.
Leon Osman takes a shot. Blocked by Davide Santon. Short corner worked by Leon Osman.
Jonas Gutierrez produces a left-footed shot from the edge of the area and misses to the left of the goal.
Effort from outside the penalty box by Darron Gibson goes wide left of the goal.
Free kick awarded for an unfair challenge on Steven Pienaar by Cheick Tiote. Leighton Baines crosses the ball in from the free kick, Cheick Tiote manages to make a clearance.
Cheick Tiote concedes a free kick for a foul on Marouane Fellaini. Phil Neville restarts play with the free kick.
Phil Neville gives away a free kick for an unfair challenge on Hatem Ben Arfa. Direct free kick taken by Hatem Ben Arfa. Free kick awarded for a foul by Fabricio Coloccini on Marouane Fellaini. Tim Howard takes the free kick.
26:48 Goal scored
Goal - Nikica Jelavic - Everton 2 - 0 Newcastle Nikica Jelavic gets on the score sheet with a goal from inside the penalty area high into the middle of the goal. Everton 2-0 Newcastle.
Nikica Jelavic takes a shot. Tim Krul makes a save.
Phil Neville handles the ball and concedes a free kick. Cheick Tiote takes the direct free kick.
Leon Osman takes the inswinging corner, save by Tim Krul.
Foul by Papiss Cisse on Phil Neville, free kick awarded. Phil Neville takes the free kick.
Hatem Ben Arfa concedes a free kick for a foul on Steven Pienaar. Leighton Baines delivers the ball, Effort from inside the area by Steven Pienaar misses to the left of the target.
The official flags Nikica Jelavic offside. Tim Krul takes the indirect free kick.
Foul by Demba Ba on Phil Jagielka, free kick awarded. Phil Neville takes the free kick.
The assist for the goal came from Marouane Fellaini.
15:32 Goal scored
Goal - Steven Pienaar - Everton 1 - 0 Newcastle Steven Pienaar scores a goal from just outside the area to the top left corner of the goal. Everton 1-0 Newcastle.
Foul by Papiss Cisse on Phil Jagielka, free kick awarded. Free kick taken by Tim Howard.
Cheick Tiote fouled by Phil Neville, the ref awards a free kick. Free kick taken by Tim Krul.
Cheick Tiote challenges Nikica Jelavic unfairly and gives away a free kick. The ball is delivered by Phil Neville, Header by Marouane Fellaini from deep inside the penalty area misses to the left of the goal.
Free kick taken by Tim Howard.
Booking The referee shows Cheick Tiote a yellow card.
Free kick awarded for an unfair challenge on Marouane Fellaini by Cheick Tiote.
Marouane Fellaini concedes a free kick for a foul on Mike Williamson. Free kick taken by Tim Krul.
Free kick taken by Tim Krul.
Booking The referee cautions Johnny Heitinga for unsporting behaviour.
Papiss Cisse fouled by Johnny Heitinga, the ref awards a free kick.
Unfair challenge on Cheick Tiote by Darron Gibson results in a free kick. Free kick taken by Tim Krul.
Demba Ba has an effort at goal from outside the penalty area missing to the wide left of the goal.
Johnny Heitinga challenges Papiss Cisse unfairly and gives away a free kick. Free kick crossed left-footed by Hatem Ben Arfa.
The game gets underway.
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