The winger grabbed the winner to maintain the Foxes’ 100% record in Europe and keep them top of Group G.
They are five points clear of Porto, the 2004 winners, and five and nine points ahead of FC Copenhagen and Club Brugge respectively with three matches remaining.
“It was an unbelievable atmosphere once again,” captain Wes Morgan told BT Sport 3 last night.
“It’s night like this you live for.”
Victory in Copenhagen in two weeks would put the Foxes through to the last 16. Mahrez said: “We’ve got nine points so we’re confident (of qualifying for the last 16).
“We just have to keep going as we did today and in the first two games.”
Leicester needed Kasper Schmeichel, who is yet to concede a goal in the competition, to produce an outstanding late save to thwart Andreas Cornelius.
A third straight Champions League win is in stark contrast to their Premier League form and Claudio Ranieri’s side have more points in Europe, nine, than they have domestically, eight.
But they are revelling in their European tour and ended Copenhagen’s 23-match unbeaten run which stretched back to May.
Mahrez had been recalled after starting Saturday’s 3-0 defeat at Chelsea on the bench as Ranieri prioritised Europe.
Following comfortable and deserved wins over Club Brugge and Porto, FC Copenhagen offered the Foxes a sterner test with the visitors six points clear in the Danish Superliga.
With Leicester sloppy in possession, the misfiring Jamie Vardy and recalled Slimani had little early service, although Vardy did see a deflected effort skid wide after 18 minutes.
Schmeichel comfortably claimed Federico Santander’s low strike and slowly Wes Morgan and Roberto Huth got to grips with FC Copenhagen who, for all their organisation, struggled to make serious inroads against the Foxes.
The Foxes continually went long and looked out of ideas before they finally worked the ball wide and were rewarded with a 40th-minute winner.
All of the joy Vardy had got came from the left flank and when he was given time the striker launched a deep cross to Slimani.
The Algerian nodded down for the onrushing Mahrez, who escaped Mathias Jorgensen, to stab in his third Champions League goal of the season from six yards.
But FC Copenhagen almost hit back instantly when Youssef Toutouh’s strike hit Morgan to loop onto the roof of the net and, from the resulting corner, Cornelius’ header dropped inches wide.
Despite their lead Leicester were still not at their fluent best but thought they had doubled their lead after 67 minutes only for the offside flag to deny Slimani a second.
Copenhagen they began to mount a late recovery and William Kvist fired straight at Schmeichel with eight minutes left before Santander’s header was deflected over.
Schmeichel was called on to make a stunning save with a minute left to secure the points when he brilliantly changed direction to keep out Cornelius’ low 10-yard strike.
Schmeichel, Simpson, Morgan, Huth, Fuchs, Mahrez (Amartey 90), King, Drinkwater, Albrighton, Slimani (Ulloa 88), Vardy (Okazaki 85).
Olsen, Ankersen (Gregus 87), Jorgensen, Johansson, Augustinsson, Verbic (Jensen 66), Kvist Jorgensen, Delaney, Toutouh (Pavlovic 85), Santander, Cornelius.
Nicola Rizzoli (Italy).