Youri Tielemans had opened the scoring for the visitors early on with a stunning strike, driving an unstoppable first-time effort into the back of the net from outside the box.
Brentford then pressed for a winner, but were caught out by a quick Leicester attack in the 73rd minute.
Tielemans played a great ball to send substitute Patson Daka away and he squared for Maddison to fire home.
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