Alexander Isak has now scored seven Premier League goals this season, more than any other Newcastle player.
Newcastle emphatically halted a run of four Premier League games without victory as Eddie Howe's team inflicted a first defeat on new Leicester manager Ruud van Nistelrooy.
The Magpies dominated the first half and took the lead when Jacob Murphy, who had already spurned two good opportunities to put the home side ahead, fired low into the corner following a clever corner routine.
Alexander Isak shot too close to Mads Hermansen in a one-on-one with the Leicester goalkeeper, but the hosts remained on the front foot in the second half and were 3-0 up within five minutes of the restart.
Bruno Guimaraes headed in from close range following another well-worked set-piece, before Isak nodded home from a similar position after Lewis Hall's cross was deflected into his path by Conor Coady.
Murphy fired over the crossbar not long afterwards and Isak sidefooted straight at Danny Ward – a half-time substitute for Hermansen – but the Magpies' winger eventually made it 4-0 with a low drive past the substitute keeper.
The hosts could have rubbed further salt into Leicester's wounds late on as Sandro Tonali fired into the side-netting and former Foxes forward Harvey Barnes curled a left-footed shot wide of the far post.
Victory lifted Newcastle up to 11th, while Leicester remain precariously placed in 16th spot, two points above the bottom three.
Magpies find scoring touch for stylish success
Saturday's success was only the Magpies' third in the Premier League since mid-September, but such is the congestion in the middle part of the table that they remain on the periphery of the European places heading into a key run of fixtures.
Whether Howe's team can finally generate some momentum remains to be seen, but there were positive signs here as they caused the Foxes numerous problems down the left-hand side in the first half.
Gordon was particularly lively, forcing Hermansen into a brilliant one-handed save inside the first 10 minutes before teeing up Murphy for the opener.
They should have been further ahead at the break, but any fears the home fans may have had about Newcastle's first-half profligacy coming back to haunt them were firmly put to bed early in the second period thanks to the close-range finishes from Guimaraes and Isak.
Tonali and Barnes could have got in on the act, but Murphy's second of the game proved to be the final flourish on a near-perfect afternoon for the hosts, who ended the game with 27 attempts and 11 on target.
After travelling to Ipswich next weekend, the Magpies face fellow European hopefuls Aston Villa, Manchester United and Tottenham in their subsequent three league fixtures.
First up, however, is Wednesday's home Carabao Cup quarter-final against Brentford, who beat Newcastle in the Premier League just last weekend.
Foxes outplayed and collapse will add concern
After back-to-back home games, this was arguably Van Nistelrooy's biggest test of his brief Leicester reign so far – but the Dutchman's side were second-best all over the pitch at St James' Park.
Other than a late spell of pressure before the interval, they failed to threaten Martin Dubravka's goal and could count themselves fortunate not to have lost by more.
Van Nistelrooy was not helped by the absences of the injured Wilfred Ndidi and the suspended Boubakary Soumare, with Hamza Choudhury drafted into midfield for his first Premier League start in more than two and a half years.
He may, however, feel aggrieved at referee Thomas Bramall's decision not to book Guimaraes for going down too easily under Jannik Vestergaard's first-half challenge in the area, with the Brazilian then cautioned just moments later for a tackle on Stephy Mavididi.
Before half-time substitute stopper Ward had even touched the ball, Guimaraes had made it 2-0.
Whether the midfielder should have been on the pitch or not, the manner of Leicester's second-half collapse will alarm the Dutchman, who cut a frustrated figure for the majority of the contest as his team were outplayed in every department.
The Foxes welcome second-bottom Wolves to the King Power Stadium next weekend in a crucial encounter, before games against leaders Liverpool and Manchester City in late December.
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