The Foxes Premier League title defence already looks doomed, but they have continued to be a force in Europe and continued their fine start with a hard-fought victory against the Danish champions.
Riyad Mahrez got the only goal of the game as Copenhagen pushed them all the way, but the win leaves Leicester on nine points from three games and knowing a win in the corresponding fixture on November 2 will ensure they qualify for the last-16 with two games to spare.
Copenhagen had the first chance of the game in the third minute when Federico Santander managed to get the better of Robert Huth and fired in a low effort which Kasper Schmeichel got down to save at his near post.
The Danes continued to enjoy plenty of possession, although Jamie Vardy had a sight on goal on 18 minutes but his fierce drive rebounded off the legs of Mathias Jorgensen.
Copenhagen stepped up another gear and Wes Morgan did well to get across and head behind a dangerous cross from Ludwig Augustinsson on 23 minutes.
Leicester managed to weather some pressure from the visitors and then took the lead five minutes before half time when Vardy’s cross was knocked down by Islam Slimani to his fellow Algeria international, Mahrez, who flicked the ball in from close range with his left foot.
Copenhagen almost replied before the break but Yussef Toutouh’s deflected strike dropped just over, before Andreas Cornelius’ header from the resulting corner also went over the bar.
Leicester started the second half brightly with Mahrez firing an effort high over from a good position and minutes later Danny Drinkwater went closer with a strike which dipped just over the bar.
The Foxes had the ball in the net on 69 minutes when Marc Albrighton played in Slimani whose first effort was pushed onto the crossbar by Robin Olsen only for the striker to head in the rebound before turning to see the offside flag harshly up against him.
Copenhagen’s first real chance of the half came on 86 minutes when Peter Ankersen’s cross was met by the head of Santander but he headed over under pressure from Danny Simpson.
Schmeichel then brilliantly saved the Foxes in the 90th minute as he managed to push away Andreas Cornelius’ effort from Santander’s cross from the left with an outstretched hand.