A double from Jacob Murphy and goals from Bruno Guimarães and Alexander Isak gave Eddie Howe's side the desired response to defeat at Brentford in their previous game - and set them up nicely for Wednesday night's Carabao Cup quarter-final clash with the Bees.
And it was a Ruud awakening for Leicester, who had picked up four points from two games under new manager Ruud van Nistelrooy but had no answer to United's slick attacking play as the Magpies recorded their biggest win of the campaign so far.
With Nick Pope injured, Martin Dúbravka came in for his first Premier League appearance of the season but the Slovakia international barely had a shot to save as Newcastle dominated.
Dúbravka's opposite number, Mads Hermansen, made a great save to deny Anthony Gordon in the eighth minute after a direct run and powerful strike from the England ace.
The resulting corner was played short to Gordon, who whipped in a cross which was met by the head of Dan Burn, but his effort went just over.
Then the lively Gordon burst down the left, but his cross evaded Guimarães. And Gordon was involved again in the 13th minute, backheeling the ball to Lewis Hall on the left - but Guimarães could only divert the full-back's dangerous cross over the bar.
Guimarães was another player who seemed to be at the heart of most of United's attacking moves and in the 18th minute he cracked in a shot, but it was too close to Hermansen.
Two minutes later, Isak ran from his own half and fed Murphy, despite being fouled by Oliver Skipp. Murphy shot wide but play was brought back for a free kick and Sandro Tonali's shot from the set-piece was blocked. Play was recycled and Murphy centred from the right, but Burn's header was deflected wide by Jannik Vestergaard.
Joelinton saw a shot from distance comfortably saved before Isak brilliantly teed up the Brazilian; his shot was bravely blocked by Hamza Choudhury, then Murphy curled an effort the wrong side of the far post when the ball fell to him.
But Murphy opened the scoring on the half-hour mark. Hall played a short corner to Tonali, who found Gordon and his cut-back was perfect for Murphy to stroke the ball beyond Hermansen from 14 yards.
The Magpies had a big opportunity to double their advantage in the 37th minute; Isak's touch was perfect as he raced onto a superb threaded Joelinton pass, but his finish was weak and Hermansen was able to save.
However the Foxes goalkeeper came off at half time, with Danny Ward replacing him between the posts. And within seconds of his introduction, the Wales international was picking the ball out of his net as Gordon's deep free kick was headed across goal by Hall and forced home by Guimarães for his first goal of the campaign.
Then came the third, as Isak was in the right place to nod past Ward as Hall's left-wing cross deflected off Conor Coady.
Isak then received a pass from Hall and danced goalwards before playing in Murphy, but the winger's shot was always rising.
Dúbravka was finally tested in the 55th minute, diving to his left to hold a Kasey McAteer strike, but it was the home side on the front foot after that as Murphy set up Isak, but his effort was straight at Ward.
Isak returned the favour on the hour, turning Vestergaard inside out before playing in Murphy, and his shot was low and hard and zipped past Ward before the goalkeeper had a chance to react.
In the 73rd minute, Tonali hit the side-netting with an acrobatic attempt before substitute Harvey Barnes cut in from the right and shot narrowly wide against his former club.
Barnes had another effort saved after good work from fellow sub William Osula, then another in the 85th minute from outside the box, but Ward was equal to it. Barnes then turned provider, digging out a cross which Hall headed wide.
A fifth booking of the season for Joelinton which means he will serve a one-game ban against Ipswich next weekend was the only disappointment, but it was a hugely positive afternoon for Howe and his team ahead of their midweek cup tie on Tyneside.