Mahrez's athletic 40th-minute volley at the King Power Stadium left Claudio Ranieri's men five points clear in Group G.
Riyad Mahrez struck to give Leicester City a third consecutive Champions League victory as the fairytale Premier League champions edged FC Copenhagen 1-0 on Tuesday.
Mahrez's athletic 40th-minute volley at the King Power Stadium left Claudio Ranieri's men five points clear in Group G with a 100 percent record and they are still to concede a goal in the competition.
With Porto winning 2-1 at Club Brugge in the other group game, Leicester will be assured of a place in the last 16 if they win away to Copenhagen in their next match on November 2.
"We're in a good position now," said Ranieri, whose side are guaranteed at least a place in the Europa League knockout phase.
"We knew it would be tough. Copenhagen tried until the end. It was difficult at the start, but the performance was good."
Leicester are struggling domestically, their title defence effectively over after four defeats in eight games, but in Europe they are rekindling memories of their 5,000-1 march to glory last season.
Their tally of points in the Champions League -- nine -- is one more than they have amassed in the league.
Ranieri was particularly indebted to his Copenhagen-born goalkeeper Kasper Schmeichel, who brilliantly swatted away a shot from Andreas Cornelius with seconds of normal time remaining.
"It was an amazing save from Kasper Schmeichel at the end," Ranieri said. "We deserved the clean sheet tonight."
It was a first defeat in 24 matches for Stale Solbakken's Copenhagen, but they remain in second place ahead of next month's return fixture.
"I'm disappointed with the result," said Solbakken. "We slept one time and it cost us the game.
"But the players have a good feeling we can beat them in Parken (Stadium) in 14 days."
With Leicester's fans a little subdued following another heavy domestic defeat -- 3-0 at Chelsea last Saturday -- it was left to Copenhagen's supporters to create the pre-match atmosphere.
The travelling fans were in fine voice and the Champions League anthem was accompanied by a burst of red flares in the away end that will almost certainly attract the attention of UEFA.
On the pitch, though, it was Leicester who carried the greater threat, despite the visitors dominating possession.
The hosts found joy with passes in behind Copenhagen's full-backs (less so when the ball was hoofed in the air towards Islam Slimani) and it was an approach that yielded the opening goal.
Five minutes before half-time, Jamie Vardy lofted a cross towards the far post from the left, Slimani headed it back across goal and Mahrez darted in to beat Robin Olsen with a close-range volley.
It was the Algerian winger's fourth goal of the season and third in three Champions League games.
Shy of a Federico Santander shot that dribbled straight into the gloves of Schmeichel, the Danish champions had not really threatened.
But they came within a whisker of equalising on the stroke of half-time when Cornelius's header from Ludwig Augustinsson's corner missed the left-hand upright by millimetres.
Cornelius menaced again early in the second half, his flick working Schmeichel, but Leicester were playing with rediscovered belief, Mahrez seeing a shot blocked by Erik Johansson.
Slimani had the ball in the net in the 67th minute when he followed in to head home after Olsen brilliantly touched his shot onto the bar, but he was denied, incorrectly, by an offside flag.
The introduction of winger Rasmus Falk lifted Copenhagen and there was one last scare before Leicester could celebrate victory.
In the last minute, Santander's low cross from the left picked out Cornelius, but Schmeichel produced a superb one-handed reflex save to keep his countrymen at bay.