Ruud van Nistelrooy, the new manager of Leicester, suffered his first loss as Newcastle decisively ended a run of four Premier League games without a win.
The Magpies controlled the first half and seized the lead after a deft corner routine saw Jacob Murphy, who had earlier missed two fine chances to put the home team ahead, strike low into the corner.
In a one-on-one with the Leicester custodian, Alexander Isak lost the ball to Mads Hermansen, but the home team continued to dominate the second half and led 3-0 inside five minutes of the resumption.
After another well-executed set-piece, Bruno Guimaraes headed in from close range, then Isak nodded home from a similar position after Conor Coady deflected Lewis Hall’s cross into his path.
Shortly after, Isak sidefooted directly at Danny Ward, Hermansen’s halftime replacement, and Murphy shot over the crossbar.
However, the Magpies’ winger finally made it 4-0 with a low drive past the substitute keeper.
Late in the game, former Foxes forward Harvey Barnes curled a left-footed drive wide of the far post, and Sandro Tonali fired into the side netting, giving the home team the opportunity to further aggravate Leicester’s situation.
Newcastle’s victory moved them up to 11th place, while Leicester is still two points above the bottom three in a precarious 16th place.