The midfielder grabbed a goal and two assists and has now netted four times in his last six games.
Youri Tielemans’ double, including a first-half penalty, marked his 100th Premier League appearance while Patson Daka also netted following a brilliant Maddison pass.
The Foxes climbed to eighth and it was also their first league clean sheet since the opening day as they overcame the early loss of Jonny Evans and recovered from Thursday’s elimination from the Europa League.
The Magpies remain second bottom, three points adrift of safety, and now face daunting games against Liverpool, Manchester City and Manchester United.
They would have hoped for last week’s 1-0 win over Burnley to be the catalyst for survival but the game turned on a controversial penalty decision when Maddison was felled by Jamaal Lascelles to allow Tielemans to open the scoring.
Up until then Newcastle were comfortable, with Jamie Vardy again named as a substitute by Brendan Rodgers having played the full game as the Foxes lost in Napoli on Thursday.
That defeat dropped them into the Europa Conference League, with Rodgers without seven players due to coronavirus or illness.
Kelechi Iheanacho, Ayoze Perez, and Ademola Lookman were already missing and the hosts’ worries worsened when Jonny Evans was forced off with a hamstring injury inside the first six minutes.
Without a senior defender on the bench Boubakary Soumare replaced him and the reshuffle saw Wilfred Ndidi become a makeshift centre-back.
Newcastle looked to take advantage and Callum Wilson’s effort deflected wide before Fabian Schar’s shot was blocked.
Leicester gradually began to see more of the ball and Maddison’s free-kick whistled over, while Martin Dubravka turned away Ndidi’s header.
Yet the Foxes were laboured in front of an unusually subdued King Power Stadium, peppered with rare empty seats.
They desperately needed a lift, with Newcastle looking comfortable, if limited, and got it six minutes before the break.
Lascelles was tempted to dangle a leg towards Maddison, who appeared to already be going down, and referee Peter Bankes awarded the penalty which Tielemans dispatched high past Dubravka.
The Magpies had reason to feel aggrieved but they needed to be bolder going forward, especially considering Leicester’s patched-up backline, to salvage anything.
Victory would have moved them level on points with Watford in 17th but Eddie Howe’s side were too tentative. Joelinton’s tame shot was gathered by Kasper Schmeichel eight minutes after the break and, soon after, Newcastle’s problems grew.
It took until the 57th minute for Leicester to really find their groove but they carved the Magpies open and a neat passing move ended with a sublime flick from Maddison to slip in Harvey Barnes.
He unselfishly squared for Daka to tap in for 2-0 and score his seventh goal in just eight starts this season.
It knocked the stuffing out of Newcastle and, while Joe Willock shot over and Allan Saint-Maximin fired at Schmeichel, there was no way back – despite Leicester’s attempts to gift them a goal with 12 minutes left.
Timothy Castagne’s overhit backpass forced Schmeichel to race back to his line and produce a sliding clearance to stop a calamitous own goal.
But Tielemans wrapped up the points with nine minutes to go when he fired in from close range, following another Maddison assist.
England international Maddison then got the goal he deserved four minutes later when he swapped passes with Daka and drilled beyond Dubravka.