Leicester maintained a perfect record in Group G in their first foray in Europe's elite club competition by edging FC Copenhagen 1 0 at the King Power Stadium yesterday with Mahrez getting the only goal of the game.
Islam Slimani headed down a Jamie Vardy cross for Mahrez to score with a close-range volley with the outside of his left foot five minutes before half-time.
With Porto winning 2-1 away to Club Brugge in the group's other game, Claudio Ranieri's side now know a win away to Copenhagen in their next match on November 2 will secure a place in the last 16. "We're in a good position now," said Ranieri.
"We knew it would be tough. Copenhagen tried until the end. It was difficult at the start, but the performance was good."
Club Brugge 1-2 FC Porto
In Bruges, Jelle Vossen put the home side in front early on but Miguel Layun lashed in the equaliser midway through the second half and Andre Silva scored a stoppage-time winner from the penalty spot.
For Porto goalkeeper Iker Casillas it was a 92nd win in the Champions League, allowing him to surpass Barcelona legend Xavi Hernandez and establish a new record.
Leicester City 1-0 Koben havn
Leicester's Premier League rivals Tottenham Hotspur found themselves hanging on for a point as they claimed a 0-0 draw away to Bayer Leverkusen in Germany in Group E.
A Vincent Janssen header that came back off the bar was the closest Spurs came to scoring at the BayArena.
The home side piled on the pressure in the second half but Javier Hernandez was denied by a brilliant save on the line by Hugo Lloris and Stefan Kiessling missed a great chance late on. "We can be pleased with the point," said Lloris.
"The game turned in the second half, Leverkusen pressed high and we struggled a bit. I think the draw is a good result for us."
Just three points separate all four teams in the section, but it is Monaco who are on top after coming from behind to draw 1-1 at CSKA Moscow.
Ivorian striker Lacina Traore, on loan from Monaco, scored against his parent club in the 34th minute but Bernardo Silva equalised for the visitors late on.
Legia Warsaw 1-5 Real Madrid
Reigning champions Real Madrid cruised to a 5-1 victory at home to Legia Warsaw in Group F after supporter violence marred the build-up to the game at the Santiago Bernabeu.
Five fans and two police officers were treated for minor injuries following clashes outside the stadium before kick-off.
When the game began, Vadis Odjidja struck the post for the visitors before Gareth Bale fired in the opener and a Marcelo shot went in off Tomasz Jodlowiec.
Miroslav Radovic pulled one back from the penalty spot but Marco Asensio made it 3-1 before the interval and substitutes Lucas Vazquez and Alvaro Morata added further goals in the second half.
Zinedine Zidane's side are level on seven points at the top of the group with Borussia Dortmund, who were 2-1 winners over Sporting Lisbon in Portugal.
Pierre-Emerick Aubameyang burst through for an early opener and a superb Julian Weigl strike made it 2-0 but Dortmund were hanging on after Bruno Cesar reduced the deficit midway through the second half.
Lyon 0-1 Juventus
In Group H Juan Cuadrado came off the bench to score a late winner as 10-man Juventus beat Lyon 1-0 in France.
Gianluigi Buffon was in fine form for the Italian champions as he saved a first-half Alexandre Lacazette penalty, while Juve had Mario Lemina sent off early in the second period.
But Cuadrado netted the winner 14 minutes from the end as the hosts failed to make their man advantage count.
"I should thank Mario Lemina for his sending-off because I thought we played better with a man less," said Juve coach Massimiliano Allegri. They are level at the top of the group with Sevilla, who were 1-0 winners away to Dinamo Zagreb in Croatia, Samir Nasri netting the only goal.