The Blues started the day with a slim chance of breaking into the top four—they needed to win and hope Liverpool lost to Brighton & Hove Albion—but they never looked likely to hold up their end of the bargain.
Dwight Gayle put the hosts ahead midway through the first half with an opportunistic finish before a quick-fire Ayoze Perez double in the second half sealed a fantastic victory for Rafael Benitez's side.
The three points secured the Magpies a hugely creditable 10th-place finish in their first season back in the English top flight.
Conte on the Brink Ahead of FA Cup Final
Antonio Conte's side looked a shadow of the team that ran out 5-1 winners against Sunderland on the final day of last season's Premier League to end the campaign seven points clear at the top of the table.
Their defensive organisation was embarrassing at times in a performance that did not bode well for the Blues' chances of lifting the FA Cup in next Saturday's final against Manchester United at Wembley.
Conte's second season in charge of Chelsea has been very different to the first.
In 2016-17, the Italian moulded a ruthless side capable of beating almost anyone. This season's edition couldn't even muster the enthusiasm for Sunday's clash even though a top-four spot was still up for grabs.
There were calls for Conte to be ousted even before the FA Cup final after the capitulation against Newcastle:
There will be no UEFA Champions League football for Chelsea next term, and even if they are able to win the FA Cup, Conte's future at the club is in the balance.
He has cut a disinterested figure on the touchline for some time now and displayed remarkable indifference after Sunday's defeat, per Goal's Nizaar Kinsella:
Benitez Stay Imperative after Impressive Finish
On the flip side, Newcastle will be desperate to keep hold of Benitez after his side secured a remarkable top-half finish with a display to savour.
Gayle took advantage of the visitors' malaise in the 23rd minute to head home from three yards after Thibaut Courtois could only palm away Jacob Murphy's looping effort.
A Chelsea onslaught early in the second half, which saw Olivier Giroud and Ross Barkley both brilliantly denied by goalkeeper Martin Dubravka, hinted at a potential rally from the visitors.
But Perez then doubled the Magpies' lead as he got a deft finishing touch on Jonjo Shelvey's long-range effort just before the hour.
Four minutes later it was 3-0 as Chelsea's defence again switched off, allowing Perez into space on the six-yard line for him to bundle home after Florian Lejeune squared Shelvey's free-kick delivery.
It was one of Newcastle's best displays of the campaign and testament to just what a brilliant job Benitez has done at Newcastle despite severely limited resources.
He has effectively guided a Championship-level side to 10th place in the Premier League and only served to enhance his already stellar reputation.
With an injection of funds over the summer the Spaniard could lead Newcastle to even better things next term, assuming he remains at the club.
Newcastle can now relax and reflect on a job well done as they comfortably remained in the Premier League without ever really flirting with relegation.
Chelsea, though, need to pick themselves up and try to salvage their season by winning the FA Cup next Saturday at Wembley against United.