Alexander Isak's header from Anthony Gordon's inch-perfect cross fired the hosts ahead, the Swede's third goal in as many competitive matches, in the early stages of the league encounter.
Eddie Howe's side then held firm to record a well-deserved clean sheet, their second in as many competitive matches after Wednesday's 2-0 win against Chelsea in the Carabao Cup, and their first Premier League victory since September.
Three changes were made from the side which defeated Chelsea as Tino Livramento, Dan Burn and Bruno Guimarães all returned to the side in place of Emil Krafth, Lloyd Kelly and Sandro Tonali respectively.
The Magpies, aiming to end a five-game winless league streak, took the lead in the 12th minute through Isak. After Gordon delivered an inviting first-time cross from the right flank, Isak rose high inside the box before guiding a delightful header beyond Gunners goalkeeper David Raya.
Newcastle withstood pressure from the visitors after breaking the deadlock despite Arsenal captain Bukayo Saka heading wide at the back post from Kai Havertz's lofted cross into the penalty area.
United went close to doubling their advantage as a neat counter-attacking move saw Jurrien Timber deflect Anthony Gordon's fizzed cross wide of the far left-hand post.
Fabian Schär preserved United's one-goal cushion shortly after as the Swiss defender turned Saka's teasing low cross into the six-yard box out for a corner before the resulting set-piece saw Lewis Hall crucially Mikel Merino's strike from point-blank range after William Saliba headed down Declan Rice's corner into the former Magpie's path.
Willock went close to netting his first Premier League goal since the previous meeting against Arsenal in February within the opening minute of the restart as the Gunners Academy graduate latched onto Gordon's pass before his lifted effort at goal was held by Raya.
Dan Burn produced an important last-ditch tackle to prevent Leandro Trossard from shooting after the Belgian forward latched onto Gabriel Martinelli's dangerous pass inside the box.
Willock was unfortunate not to extend Newcastle's lead further after the central midfielder combined with Joelinton before racing onto the Brazilian's pass and, despite beating Saliba to the ball, flashed his effort over the crossbar.
Isak was unable to net his and United's second goal of the afternoon as the 25-year-old striker picked up the ball from distance before his drilled attempt was beaten away by Raya before the loose ball bounced over the head of the incoming Gordon.
Rice went close to punishing Newcastle as the Gunners midfielder's deflected strike inside the penalty area, leaving Nick Pope stranded, trickled narrowly wide of the right-hand post.
Hall was forced to make another key block shortly after, with the 20-year-old full-back blocking Trossard's close-range strike after Rice's in-swinging corner found the winger at the back post.
With the full-time whistle nearing, Joelinton almost netted United's second goal of the afternoon as the South American leapt high from Harvey Barnes' cross but saw his headed attempt saved by Raya.
In the third of five stoppage-time minutes, Rice missed an opportunity to deny Newcastle maximum points after latching onto Saka's inviting cross from the right flank but could only direct his header wide of the left-hand post to the delight of the United supporters.
Newcastle United: Nick Pope, Tino Livramento, Fabian Schär, Dan Burn, Lewis Hall, Bruno Guimarães (Lloyd Kelly 90), Sean Longstaff, Joe Willock (Sandro Tonali 65), Anthony Gordon (Harvey Barnes 85), Joelinton, Alexander Isak.
Substitutes: Martin Dúbravka, Emil Krafth, Will Osula, Miguel Almirón, Alex Murphy, Lewis Miley.
