In the Magpies' final fixture of the campaign at St. James' Park, the hosts broke the deadlock in the second-half as Arsenal defender Ben White turned the ball into his own net following Joelinton's inviting cross.
After a dominant display from start to finish, Bruno Guimarães extended Newcastle's advantage in the closing stages as Eddie Howe's side secured a deserved victory, United's second in their previous 21 league meetings against the Gunners, to move into 12th place on 46 points.
In front of an electric home crowd, the Magpies began the contest in bright fashion and were almost rewarded with an early goal as Miguel Almirón chased down Aaron Ramsdale before the goalkeeper's intended clearance struck the Paraguayan and deflected across goal.
Newcastle saw another chance go begging as Guimarães threaded a neat pass into Sean Longstaff's path before the midfielder's fizzed cross was parried by Ramsdale, with the loose ball hooked to safety by White.
The Gunners, aiming to move into fourth place with a victory on Tyneside, went close to opening the scoring through Saka as the 20-year-old winger combined with Martin Ødegaard before his first-time effort was crucially blocked by Magpies defender Dan Burn.
Martin Dúbravka then kept United on level terms as the Slovakian goalkeeper held Saka's low strike after the Gunners forward, who scored in the reverse fixture back in November, had dangerously cut inside from the right flank.
Allan Saint-Maximin went narrowly close to breaking the deadlock before the half-time whistle as the Frenchman evaded the challenge of Takehiro Tomiyasu before his low strike was saved by Ramsdale, who got down low to push the strike out for a corner.
In the opening minutes of the second-half, Newcastle were forced into an early change as Jamaal Lascelles replaced Schär after the Swiss defender took a heavy fall following a 50-50 challenge with Arsenal striker Eddie Nketiah.
However, in the 55th minute, Newcastle opened the scoring in fortunate circumstances. As Saint-Maximin sent a pass up the left wing into Joelinton's path, the Brazilian's teasing delivery into the penalty area, targeting Wilson, was turned into the net by White.
Wilson went close to doubling Newcastle's advantage as the Coventry-born forward latched onto Guimarães' lofted cross from the byline but his venomous volley flew over the crossbar.
The Magpies continued their push for a second goal as Miguel Almirón and Emil Krafth combined neatly down the right flank before the Swedish full-back picked out Wilson, but the forward's strike deflected over the bar.
Eddie Howe introduced Ryan Fraser and Jacob Murphy from the substitutes' bench and the pair were involved in a key opportunity in front of goal as the latter intercepted a loose ball before passing to Fraser, and after the Scotsman returned the favour, Murphy's shot was fired straight towards Ramsdale.
Newcastle's chances in front of goal kept coming as Wilson's speculative long-range effort beat the stranded Ramsdale before dropping agonisingly wide of the right-hand post.
In the 85th minute, the Magpies put the game out of Arsenal's reach as Guimarães notched his fourth goal in his previous six matches.
After Longstaff cooly lifted the ball in behind the Arsenal defence, Wilson's shot was saved before Guimarães was on hand to place the ball into the net in front of an ecstatic Gallowgate End.
Following a 12th win of the term, Newcastle will now bid to equal their highest Premier League points tally since the 2013/14 campaign when they travel to Burnley on Sunday, 22nd May (kick-off 4pm BST).
Newcastle United: Martin Dúbravka, Emil Krafth, Fabian Schär (Jamaal Lascelles 48), Dan Burn, Matt Targett, Bruno Guimarães, Sean Longstaff, Joelinton, Miguel Almirón (Jacob Murphy 77), Allan Saint-Maximin (Ryan Fraser 77), Callum Wilson (Dwight Gayle 90).
Subs not used: Karl Darlow, Kieran Trippier, Federico Fernández, Paul Dummett, Matt Ritchie.
