Tielemans struck 18 minutes from time to add to James Maddison's 55th-minute opener as the Foxes profited from two rare pieces of quality in an otherwise ordinary game which failed to light up a wintry Tyneside.
Even Jamie Vardy was strangely off key as he repeatedly strayed offside, although it was his astute pull-back which allowed Maddison to open the scoring.
Newcastle briefly gave themselves hope when substitute Andy Carroll scored his first goal for the club in more than 10 years as time ran down, but it proved to be too little, too late.
The Foxes eased into their stride from the off, with Maddison revelling in the freedom of the cover provided by Wilfred Ndidi and Tielemans to pin the hosts back, and it was he who served warning with just three minutes gone when he whipped a curling effort across the face of goal after his initial attempt had been blocked.
Tielemans and Vardy combined to carve open the home defence seven minutes later, but having taken the return pass, Tielemans opted to try to find Harvey Barnes rather than shoot and put the ball straight out of play.
Vardy had the ball in the net seconds later after expertly rounding keeper Karl Darlow, but fortunately for the Magpies, from an offside position, and the let-off belatedly sparked a response with Steve Bruce's men retaining possession for an extended period which culminated in Joelinton heading a Federico Fernandez cross straight at Kasper Schmeichel.
Newcastle's higher tempo hampered Leicester's ability to play out from the back, although they were relieved to see Wesley Fofana's header from Maddison's stoppage-time corner fly high over.
In an untidy start to the second half, neither side was able to find a telling final ball as half-chances came and went, with Vardy failing to beat the Magpies' offside trap once again and Miguel Almiron unable to pick a hole in the Foxes' rearguard with Callum Wilson bursting into space.
However, Leicester finally carved out a decisive opening 10 minutes after the restart when, after Almiron had lost possession high up the field, Barnes broke at pace to feed Vardy, who cut inside before teeing up Maddison to blast past the helpless Darlow.
Maddison and Barnes both went close as the visitors sensed an opportunity to kill the game off, and they looked to have done just that with 18 minutes remaining when Marc Albrighton found space on the right before picking out Tielemans and watching him sweep home without breaking stride on the edge of the box.
Carroll briefly threatened to spoil Leicester's day after volleying his first Newcastle goal since Boxing Day 2010 with nine minutes left on the clock, but the 2016 champions saw out time with little difficulty.
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