After a goalless first-half at St. James' Park, Newcastle fell behind after the hour mark following Carlos Alcaraz's header in front of a stunned Gallowgate End.
However, with Nottingham Forest and Aston Villa both losing their respective fixtures against Chelsea and Manchester United, the Magpies secured a place in European football's most prestigious club competition for a second time in their last three seasons.
Eddie Howe made one change to the starting XI which suffered a narrow 1-0 defeat against Arsenal last weekend as top goalscorer Alexander Isak led the line in place of Callum Wilson.
Wearing the new adidas home kit for the 2025/26 season, Newcastle were unable to muster a shot on target in the opening stages of the league encounter, with Gordon's curling strike from the edge of the box flying over the crossbar before Nick Pope held Alcaraz's long-range free-kick before the half-hour mark.
Nick Pope, targeting a fourth consecutive Premier League clean sheet at St. James' Park, produced an important stop to prevent James Garner breaking the deadlock after the Toffees midfielder initially intercepted Bruno Guimarães' pass before his resulting shot from the edge of the penalty area was pushed away to safety by the United shot-stopper.
Sandro Tonali went close to netting a fourth goal in his last six home games as the Italian midfielder's vicious strike from distance was beaten away by Jordan Pickford before Isak's rebound was turned around the post by the former Sunderland goalkeeper.
Sven Botman was unfortunate not to score his first goal at St. James' Park after the Dutch centre-back was denied twice in quick succession, with his header from Tonali's dangerous corner pushed over the bar by Pickford before the 25-year-old's close-range effort shortly after was turned out for a corner by Pickford's left leg.
Pope recorded another vital stop to deny Alcaraz as the Argentine rose high from Vitaliy Mykolenko's teasing cross from the left flank before his powerful header was brilliantly tipped over by the England international.
In the second half, Pope denied Alcaraz for a second time after the South American was allowed time and space to drive forward before his resulting low drive was pushed around the post by the alert goalkeeper.
However, in the 65th minute, Everton took the lead through Alcaraz, who leapt from Mykolenko's lofted cross into the box before heading the ball into the bottom right-hand corner.
Isak went close to drawing United level in swift fashion as the Swedish frontman collected the ball from distance before his powerful long-range drive was beaten away by Pickford before, minutes later, volleying the ball over from Kieran Trippier's corner.
Targeting a late leveller, Fabian Schär tried his luck from distance as the Swiss defender rifled a powerful effort wide of the left-hand post before Kieran Trippier's bending free-kick flew wide of the target.
Pope was on hand to prevent Dominic Calvert-Lewin doubling Everton's lead in stoppage-time as the Blues striker's strike inside the box was blocked by the body of the Magpies goalkeeper.
Schär went agonisingly close to equalising in the closing stages after turning William Osula's low cross wide of the right-hand post from close-range before Bruno Guimarães saw a stabbed effort from the edge of the box tipped over the crossbar by Pickford.
Despite ending their six-game unbeaten streak at St. James' Park, Newcastle secured fifth place in the English top-flight to secure their passage into next season's Champions League to cap off, arguably, the club's greatest season in living memory.
