The Magpies took the lead in stunning fashion after the half-hour mark, with Bruno Guimarães scoring directly from a corner kick, before Burnley were reduced to ten men following Lucas Pires' straight red card after committing a last-man challenge on Anthony Elanga.
Anthony Gordon's penalty doubled the Magpies' lead on the stroke of half-time, netting his second successful spot-kick in as many matches and despite Zian Flemming's stoppage-time penalty halving the deficit, the Magpies saw out the contest to record maximum points, with Yoane Wissa also making his highly-anticipated debut from the substitutes' bench.
Eddie Howe made six changes from the side which claimed a 2-2 draw against Tottenham Hotspur, with Wissa named in United's matchday squad for the first time since his transfer from Brentford in September.
The visitors created the opening goalscoring opportunities as Tino Livramento's intended clearance from inside his own box was blocked, forcing Magpies goalkeeper Aaron Ramsdale into importantly holding the inadvertent effort at goal, before Burnley striker Lyle Foster's curling effort from the edge of the box minutes later flew wide of the target.
Newcastle went close to opening the scoring as Joe Willock regained possession in a dangerous position and after neat build-up play involving Guimarães and Jacob Ramsey, the latter teed up Nick Woltemade inside the box before the German striker's powerful goalbound drive was blocked by Maxime Estéve's head.
Burnley hit the crossbar shortly after as a dangerous corner from the right flank was contested between Estéve and Ramsdale inside the six-yard area before the ball dropped onto the bar before Hjalmar Ekdal turned the loose ball wide from closer-range.
Newcastle, targeting a seventh league win in succession against the Clarets, took their turn to hit the woodwork as Gordon went agonisingly close to netting an impressive strike, with the Liverpool-born winger's fizzing effort from the edge of the box flying beyond former Magpies goalkeeper Martin Dúbravka before clipping the far right-hand post.
In the 31st minute, Newcastle took the lead through Guimarães' fifth goal in his last eight league games on home soil as the Brazilian midfielder's in-swinging corner from the left wing evaded Dúbravka before landing into the bottom right-hand corner.
Elanga was unable to net his first Newcastle goal since joining the Magpies from Nottingham Forest last summer, as the Sweden international initially failed to make contact with Gordon's teasing cross into the box but despite retrieving the ball, saw a fierce strike at goal blocked out for a corner.
With the half-time whistle approaching, Burnley were reduced to ten men as Elanga raced through on goal, following Gordon's delightful pass, before being brought down by Pires on the edge of the penalty area, with the Brazilian full-back receiving a straight red card from referee Stuart Attwell.
Newcastle were awarded a penalty before the break as, following a VAR review, Burnley midfielder Lesley Ugochukwu was adjudged to handle Gordon's lofted cross from the byline before the Magpies winger converted from 12 yards with ease, sending Dúbravka the wrong way.
Guimarães almost netted his second goal of the afternoon as the Magpies captain's impressive strike from the edge of the box, with his outside of his foot, forced the busy Dúbravka into tipping the ball over his own crossbar.
Lewis Hall, introduced from the substitutes' bench after the hour mark, almost made an immediate impact in front of goal as the 21-year-old left-back combined neatly with Guimarães before his drilled shot at goal was blocked out for a corner by Dúbravka.
Gordon hit the woodwork for a second time as the 24-year-old collected on the left flank and after being awarded time and space, thrashed a thunderous effort onto the bar from the edge of the penalty area.
The home crowd rose to their feet to welcome Wissa to the pitch, with the DR Congo international handed his Newcastle debut following a long-term injury, before Dúbravka prevented Estève from heading his own net after the Slovakian 'keeper, who spent seven years at St. James' Park, tipped the defender's inadvertent effort over the bar.
Elanga went close to adding gloss to the scoreline in the final stages as the rapid right winger curled a delightful attempt narrowly wide of the left-hand post.
With three minutes of stoppage-time, Burnley were awarded a penalty as Jacob Ramsey was adjudged to handle the ball inside the box following a corner before Flemming converted from the spot despite Ramsdale guessing the correct way.
Despite a nervy finale, with Clarets substitute Josh Laurent and Flemming both unable to head the ball towards goal after the unmarked pair failed to make contact with a dangerous cross from the right flank, the Magpies extended their unbeaten run in the English top-flight to four matches.
Newcastle United: Aaron Ramsdale, Fabian Schär, Anthony Gordon (Joelinton 74), Malick Thiaw, Anthony Elanga, Tino Livramento, Nick Woltemade (Yoane Wissa 74), Joe Willock (Lewis Miley 63), Dan Burn (Lewis Hall 63), Bruno Guimarães (c), Jacob Ramsey (Sandro Tonali 90).
Substitutes: John Ruddy, Harvey Barnes, Jacob Murphy, Alex Murphy.
