Leicester found the net either side of halftime through a penalty from Tielemans and a tap-in from Zambian forward Patson Daka. Tielemans and James Maddison scored late on to condemn Newcastle to their eighth defeat of the season.
Tielemans scored from the spot shortly before the break after Maddison had been tripped by Newcastle defender Jamaal Lascelles. Leicester doubled their lead in the 57th minute when Maddison found Harvey Barnes who ran through on goal and laid it off for Daka to score.
Newcastle barely threatened Kasper Schmeichel's goal and the closest they came to scoring was through Leicester defender Timothy Castagne when he overhit a back pass to the Danish keeper who had to race back and clear the ball off the line.
Tielemans got his second late on, hitting the ball into the roof of the net from close range, before Maddison put a gloss on the scoreline with his fourth league goal of the season.
Eddie Howe's Newcastle are 19th in the standings, only kept off the bottom thanks to Norwich City's worse goal difference. Leicester climbed to eighth.