Belgium international Tielemans hit a stunning long-range strike to open the scoring for Brendan Rodgers’ side.
Mathias Jorgensen hauled Brentford level but Tielemans then helped tee up Maddison’s first goal since February to secure three points for the visitors.
Victory rounded off a satisfying week for Leicester boss Rodgers following thrilling wins over Manchester United and Spartak Moscow.
In fact the only thing that could make it sweeter would be the news that Tielemans, one of the most coveted midfielders in Europe, had agreed a new deal.
His current contract expires in 2023 so the Foxes fear they will have to sell their prized asset next summer or risk losing him for nothing a year later.
Tielemans’ representatives remain in talks, and their hand will be even stronger after the 24-year-old’s latest display, turning the game on its head after Brentford had bossed the early stages.
The Bees almost took the lead inside the opening two minutes when Christian Norgaard hooked the ball goalwards, with fellow Dane Kasper Schmeichel diving low to his left to claw the ball away.
Then Ivan Toney had the ball in the net from Rico Henry’s square ball, but the striker was flagged offside, before Bryan Mbeumo skewed a good chance wide, all within the space of a breakneck opening 10 minutes.
But it was Leicester who took the lead with their first sight of goal in the 13th minute, a headed clearance from Henry falling to Tielemans who lashed it home from 25 yards.
The goal knocked the stuffing out of Brentford and Maddison almost doubled the lead with a curler which flew just wide of David Raya’s left-hand post.
The Foxes squeezed the life out of the remainder of the first half until Toney met a cross from Frank Onyeka, forcing Schmeichel to tip his header over the crossbar.
After the interval Raya pushed away another long-range Maddison strike with substitute Patson Daka, on for Jamie Vardy, unable to convert the rebound.
Raya also palmed Boubakary Soumare’s drive over while, at the other end, Toney planted a header too close to Schmeichel.
Brentford’s equaliser came on the hour mark, Jorgensen rising at the near post to glance in Mathias Jensen’s corner.
But the Bees’ defence was picked apart by Tielemans’ through-ball in the 73rd minute, allowing Daka to race clear and square the ball for Maddison to tap into an empty net and seal another three points.
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