Maddison fired home the first goal at St. James’ Park of the new calendar year, before Tielemans swept home a second to leave Steve Bruce’s men with plenty to do in the final 20 minutes.
Substitute Andy Carroll volleyed home his first goal since returning to the club in 2019 to give United hope late on, but a comeback didn’t materialise despite their late rally.
The visitors were quickest out of the traps, with Maddison – who scored a stunning goal as his side won at St. James’ Park last season – took aim from the edge of the box, but his left-footed shot flashed wide of Karl Darlow’s upright.
The Foxes looked dangerous on the break, though, and with better timing they could have led early on. Jamie Vardy was a constant threat but the former England frontman’s first involvement was to help engineer a shooting opportunity for Tielemans, but the Belgian took too long to shoot and his lay-off, intended for Harvey Barnes, was too heavy.
United may have been saved by the offside flag on that occasion anyway, and they certainly were two minutes later. Vardy stole in behind the Magpies’ backline before rounding Karl Darlow and finishing well from an acute angle, but the goal was disallowed.
It was a warning for Bruce’s side, but they responded reasonably well, with Federico Fernández’s cross finding Joelinton in the box. The Brazilian beat his marker to it but Kasper Schmeichel was equal to it, saving with ease.
Leicester still looked the most likely to strike before the break, though, with one flowing move cumlimating in Timothy Castagne’s cross ricocheting off Barnes before dropping wide and Wesley Fofana nodding over, but it remained goalless at half-time.
Vardy spurned the first big chance after the restart, slicing wide after being played in over the top by Castagne, while Miguel Almirón volleyed well over at the other end as the contest remained relatively open.
But 10 minutes into the second period, the Foxes pounced. It owed much to the acceleration of Barnes, who ran at the United defence and slipped in Vardy on the left. His cutback found Maddison arriving in the box, and he thumped a first time finish high into the net beyond Darlow.
Maddison tired his luck again moments later with a swerving first-time shot which drifted past the post and Barnes saw an effort charged down either side of some promising Newcastle breaks, which resulted in dangerous crosses from Matty Longstaff and substitute Jacob Murphy.
But with 18 minutes remaining, it was two. It was another swift attack from Brendan Rodgers’ side, and it ended in a fine finish from Tielemans, who hammered home Marc Albrighton’s cutback from just outside the box.
Carroll was summoned from the bench as the Magpies sought a way back and he made an immediate impact, blasting home a terrific low volley on 81 minutes after Matt Ritchie’s free kick was only cleared back into his path.
It set up an intriguing end to the game but despite plenty of late endeavour – with a Jonjo Shelvey centre zipping agonisingly across the face of goal – the Foxes held on, and Newcastle began 2021 with a loss.
