Tielemans then added his second of the afternoon with nine minutes remaining and James Maddison's composed finish sealed a clinical 4-0 victory.
The result sees Leicester move up to eighth in the Premier League table, while Newcastle remain 19th with 10 points from 16 matches.
Story of the game
Brendan Rodgers made two changes from the UEFA Europa League defeat to Napoli as Luke Thomas replaced Ryan Bertrand at left-back and Daka surprisingly started up front ahead of top scorer Jamie Vardy, who was only named on the bench.
Though, The Foxes were forced to name three players without a senior appearance on the bench due to illness and covid-related issues.
Newcastle started the game with a positive attitude and put pressure on the hosts defence, who looked shaky in the opening exchanges, but despite enjoying a bright spell, they failed to test Kasper Schmeichel.
The Foxes began to enjoy the possession and were awarded a free-kick in a dangerous position on 15 minutes, when Joe Willock brought down Harvey Barnes outside the box, but Maddison's effort flew just over the crossbar as it rippled the top netting.
Maddison was given a second chance from another set piece opportunity, after Jamal Lewis tripped Daka, but the midfielder's inviting delivery was met by Ndidi at the back post and his header was kept out by a strong left hand from Martin Dubravka, despite it going wide.
Seven minutes before the break, the hosts were given a controversial penalty after Jamaal Lascelles stuck out a leg and Maddison made contact with it, and VAR agreed with Peter Bankes' initial decision.
Tielemans stepped up and emphatically rifled the ball into the top-right corner confidently sending Dubravka the wrong way as Rodgers' side held on to a slender half-time lead.
The Magpies' first shot on target came on 53 minutes, as Joelinton's long-range strike was comfortably gathered by Schmeichel.
Leicester heaped more misery on the visitors and doubled their advantage in style as Maddison flicked on a sensational first-time pass into the feet of Barnes, who was through on goal and the 24-year-old pulled it back for Daka for the simplest of finishes into an empty net.
Murphy almost made an instant impact coming off the bench as he fired the ball towards Schmeichel from a narrow angle, and the Danish goalkeeper kicked it into the path of Jonjo Shelvey on the edge of the box, but his shot was well blocked by Ndidi.
Timothy Castagne nearly gifted The Magpies a way back into the game, albeit in bizarre circumstances, as the Belgian's heavy back-pass caught Schmeichel by surprise, but Leicester's number one raced back and hooked the ball off the line.
The Foxes then still had time to add to Newcastle's woes with two late goals in the space of four minutes as Tielemans was left unmarked and added his second with a powerful finish into the roof of the net, before Maddison combined with Daka to score his sixth goal of the season and round off a magnificent 'Man of the Match' performance.
Leicester earn first top-flight clean sheet since August
It was on the opening day of the season when The Foxes last claimed a Premier League clean sheet in a 1-0 win over Wolves. Prior to the match, Leicester had conceded at least twice in their past five top-flight games at the King Power Stadium so this clean sheet in particular will feel all the more sweeter.
With several of their players missing through illness and covid-related issues, along with the early injury that Evans picked up, Leicester will be praying that they don't receive any more bad news in the coming weeks.
A key penalty decision doesn't go in the Magpies' favour
The big talking point from a Newcastle perspective was the awarding of the Leicester spot-kick. While Lascelles' leg was outstretched, Maddison cleverly knew that if he made any contact with it, the decision would likely go his way and so it did.
However, despite a promising start where they made it uncomfortable for Leicester's defence, Newcastle only registered three shots on target and with a brutal set of fixtures coming up over the festive period, they may regret not troubling Schmeichel more, given the damage the scoreline has done to their goal difference.
Leicester City: Schmeichel; Castagne, Evans, Soyuncu, Thomas; Tielemans, Ndidi; Maddison, Dewsbury-Hall, Barnes; Daka. (4-2-3-1)
Newcastle United: Dubravka; Manquillo, Schar, Lascelles, Lewis; Almiron, Shelvey, Willock, Saint-Maximin; Wilson, Joelinton. (4-4-2)