Callum Wilson's close-range opener was his 47th league goal for the Magpies, moving him beyond Peter Beardsley's tally and making him the club's second-highest Premier League goalscorer of all-time - with only Alan Shearer ahead of him.
Sean Longstaff's well-taken second put the Clarets firmly on the back foot and by the time Bruno Guimarães coolly made it 3-0 before half time, the relegation-threatened hosts were crumbling.
In the second half, Alexander Isak netted his 24th goal of the season after seeing his penalty saved moments earlier to compound Vincent Kompany's side's misery, with Dara O'Shea's late consolation the only blemish on an otherwise emphatic display and result for those in black and white.
Burnley actually began brightly, taking the game to visitors in the early exchanges. Jacob Bruun Larsen saw his effort smothered by Martin Dúbravka and only Dan Burn's perfectly-timed sliding challenge prevented Lyle Foster from going one-on-one with United's Slovakian stopper.
Guimarães' nudge on Lorenz Assignon brought appeals for a penalty from the hosts, which were ignored by Anthony Taylor, and the lively full back's curling effort was held by Dúbravka soon after.
But with 19 minutes gone, and against the run of play, Howe's side struck. Tino Livramento's burst upfield led to a Jacob Murphy cutback which Isak looked set to convert. His finish was blocked by goalkeeper Arijanet Muric, though, and Wilson was on hand to swiftly turn home the rebound from close range.
It was a landmark goal for the England frontman, and once that opener went in, the floodgates began to open. Livramento saw a firm strike parried by Muric and Anthony Gordon flashed another wide but with ten minutes left in the half, Newcastle grabbed a second. They had enjoyed some success down the right and after a break from Lewis Hall had pushed them up, Murphy's cutback from that flank was swept home by Longstaff for his seventh of the campaign.
Four minutes later, it was three. Burn stole possession in the final third, allowing Gordon to get into the box. His assist for Guimarães was neat and the Brazilian's low finish was precise. They could even have had a fourth before the break, but when another Murphy centre from the right found Emil Krafth, the defender stumbled as he tried to get his shot away.
Things almost became worse for Burnley after the restart. Isak's first spot-kick - awarded by Taylor after Josh Brownhill had clumsily bundled Gordon over in the box - was kept out by Muric down low to his right. The Clarets then survived a VAR check for encroachment - but almost as soon as Taylor had been informed the alleged offence had been no material effect, Kompany's men were rapidly undone again. Murphy's pace saw him scamper free of the backline down the right again, and his cross was sidefooted home by Isak, just after it narrowly evaded Wilson in the middle.
Guimarães nearly grabbed a second, as his curling shot was palmed away by Muric as it looked to be heading into the top corner, while Sander Berge thumped a rare Burnley shot just beyond Dúbravka's upright in an isolated moment of pressure from the hosts.
But this was about as comfortable as it gets for Howe and his team, who eased to victory on a rainy afternoon in Lancashire - and the travelling supporters who made the journey were further rewarded when Joelinton made his long-awaited return from injury - along with the fit-again Miguel Almirón - as a substitute, shortly before O'Shea's looping header pulled one back for the hosts.
