Joe Willock's delightful goal was the difference in the game as the Magpies beat the Blues.
Eddie Howe's rejuvenated side regained third spot before the World Cup break, and will be in a European place at Christmas for the first time in over a decade.
A fifth successive Premier League win, against an out-of-form Chelsea, was achieved with the help of a solidity and fluency that their opponents could not match.
After working hard in the first half, Willock finally found a breakthrough when he curled in from 18 yards after a surging run by Almiron.
After the introduction of Christian Pulisic, a youthfulChelsea improved in the second half.
After their third consecutive loss in the league, they have fallen to eighth in the table, eight points behind fourth-place Spurs.
This was a match that demonstrated the rapid progress made by Howe's side in the 13 months since the club's takeover and the team celebrated with their fans at the final whistle.
Dan Burn and Kai Havertz were involved in an altercation after the final whistle, and angry players continued to argue as they left the field.
The players headed down the tunnel with huge smiles on their faces after a win that could make their fans dream of a European campaign.
The result of having Bruno Guimaraes in the middle was that they showed more fluency than their opponents.
But with Chris Wood preferred to the rested Wilson up front, Newcastle failed to truly test the visitors before the break, with top scorer Almiron flashing a volley over. They had a penalty appeal waved away by the referee after the ball hit the man.
Longstaff's effort was saved by Mendy and the hosts should have taken the lead shortly after half-time when Almiron's cross was nodded back byJoelinton.
A surging run from Almiron, who has scored seven goals in seven games, helped set up Willock's curling strike.
It is no surprise that the teams that have recently gone through takeovers are more advanced than the ones that haven't.
The result, performance and feeling around the ground on Saturday felt like Howe's side are already built to challenge the premier league hierarchy, despite the new owners preaching that their evolution will take time.
Fans of both clubs will be wondering what is happening to their teams after they headed home from the last game.
There was a lot of effort from the visitors, but once again an unpredictable Potter team selection looked disorganized, with three players performing at right wing-back at different points during the game.
There was little they could do about Ruben Loftus-Cheek's early injury, but after Cesar Azpilicueta was withdrawn at half-time, there was nothing they could do.
Lewis Hall made his premier league debut at left wing-back with Almiron. The 18-year-old had time to support the others.
He set up Broja for a shot that failed to test Pope in the goal, and played a part in another attack where he almost connected with Mount.
Thiago Silva was the one who steered them through the first half after the Brazilian replaced Rubens-Cheek.
The unsavoury scenes at the end of the game were caused by the desperation of the visitors to find an equalizing goal and pointed to an unhappy camp with further questions for Potter.