In a game lacking in clear-cut chances, Riyad Mahrez netted the decisive goal with five minutes left of the first half and his side were able to hold on for the remainder of the game in the East Midlands.
Claudio Ranieri's side now only require one more win to guarantee their place in the last 16 of the competition.
Read below to see how the action unfolded at the King Power Stadium.
6.49pmWatching Leicester in the Champions League still takes a bit of getting used to but if Claudio Ranieri has his way, we will be seeing the Foxes in the competition after Christmas. This week, the Italian has openly stated that his short-term priority is ensuring that his team make it through to the last 16 of the competition and he could achieve just that if his team get the better of Copenhagen this evening.
6.52pmRegardless of tonight's result, there would still be work to do to reach the second round of European football's premier tournament but their progress would be made much easier with three points over their closest rivals in Group G. Porto are sure to still have their say later in the group but for now, Leicester must focus on securing the win that would move them to the brink of at least a top-two finish.
6.53pmAnyway, without further ado, let's take a look at the team news which is coming from each of the changing rooms at the King Power Stadium.
7.00pmWe are still awaiting news of the Copenhagen bench so let's get cracking with taking a look at the Leicester team. As expected, Riyad Mahrez and Islam Slimani both return to the starting lineup but Shinji Okazaki has to make do with a place on the bench. Danny Simpson is preferred to Luis Hernandez at right-back while Andy King is given the nod over Daniel Amartey in the centre of midfield.
7.05pmAs for Copenhagen, let's take a look at the players in their squad who have previous experience of British football, shall we? We have William Kvist, who will be familiar to both Fulham and Wigan Athletic fans after playing for both clubs in 2014 and 2015. There's Andreas Cornelius who endured a disappointing spell at Cardiff City either side of playing for the Danes. On the bench, we also have Stephan Andersen, who played for Charlton Athletic between 2004 and 2007.
7.09pmAs usual, this is not the only game that we have for you this evening. If you click here, you will have access to the games in Madrid and Leverkusen as Real Madrid and Tottenham Hotspur look to get wins on the board, while you will also be able to take your pick from all the build-up to the fixtures which are taking place this tonight and tomorrow.
7.13pmThe other game in this group sees Club Brugge host Porto. If Brugge's display against Leicester is anything to go by, you would expect the Portuguese giants to ease to victory but both Leicester and Copenhagen will be hoping that Brugge can do them a huge favour.
7.16pmAt this point, we would usually take a look at the head to head record but it does not take a genius to work out that these two teams have never met in a competitive fixture. Given the make-up of the fixtures in Group G, they will be meeting again in Denmark in two weeks time.
7.21pmCopenhagen regularly find themselves qualifying for Europe but it's not too often that they find themselves in the group stages of the Champions League. They finished fourth in a group containing Real Madrid, Juventus and Galatasaray in 2013, while they reached the last 16 during the 2010-11 campaign but they are the only times in which they have come through the qualifying rounds in the past decade. Given the start they have made to this group, they will be eager to make the most of coming through their first two fixtures without defeat.
7.26pmCopenhagen's visit to the King Power Stadium will be the fifth time that the club has played a European fixture on English soil. However, they are still awaiting their first win having only registered two draws. Will it be fifth time lucky in the East Midlands?
7.30pmIt won't have gone unnoticed by many of you that Copenhagen are managed by Stale Solbakken, who last visited the Midlands when he was the boss of Wolverhampton Wanderers. Solbakken has achieved legendary status at his current club but the same cannot be said for his time at Wolves where he lasted just 30 games, 15 of which ended in defeat with his final match seeing his team humiliated by Luton Town in the FA Cup third round. He will certainly be hoping for better luck tonight.
7.32pmWe've less than 15 minutes to go until kickoff. I think it's time for a prediction...
7.35pmPREDICTION! Leicester have been poor in the Premier League for much of the season but most of their bad performances have come on the road and we think they will make home advantage count this evening. Like the Foxes, Copenhagen are a close-knit unit who will fight for every ball but we think the English outfit will have enough to come through by a 2-1 scoreline. Don't bet against a Jamie Vardy goal too - he's due one.
7.38pmWhile we are talking about Vardy, it has been seven games since he last found the back of the net. He began the season with three goals during August but they have dried up since then and he has even come in for criticism - probably unfairly - from former England striker Alan Shearer. He will feel as though he has a point to prove tonight.
7.43pmIt's time for the two team to make their way onto the pitch at the King Power Stadium. It's the kind of atmosphere which suggests both sets of supporters are keen to make the most of occasions like this.
3 minCopenhagen have had the majority of possession during these opening stages and Schmeichel has already been forced into action to stop a Santander cutback going across goal.
6 minLeicester are competing well but Copenhagen are on top here. A cross towards the two towering strikers caused problems in the penalty area before moments later, Simpson was forced to put behind for a corner.
9 minI suspected Copenhagen wouldn't be overawed tonight but they have started this game like the home side. They are spraying the ball about with intent and Leicester have a further problem because it appears that Morgan is going to have to be replaced after suffering a back injury.
13 minThere's been a goal in the other match in this group and Club Brugge have taken the lead against Porto! It is still early days but that would be a boost to both Leicester and Copenhagen. Morgan is still trying to run his back issue off but he is visibly struggling.
16 minIt's taken over 15 minutes but Leicester finally have a bit of success in the final third. However, crosses from both Vardy and Mahrez fail to find Slimani and Copenhagen eventually clear.
18 minSHOT! Vardy has come into the game over the past few minutes and he manages to send a shot marginally wide of the post via the aid of a deflection. I think Olsen would have had it covered if it had hit the target.
22 minMorgan is battling on valiantly and he's just had to dive to his right to head away a cross which was threatening to find a Copenhagen man inside the six-yard box. From the resulting corner, King was able to jump above everyone and clear. It's a decent game but we are still awaiting our first clear-cut opportunity.
27 minYou can't fault the enthusiasm from the Leicester supporters but they must be wondering whether their team is coming back down to earth. They are lacking the zip which they played with last season. Copenhagen are doing a good job of nullifying their attacking threat but there's not a lot of urgency from the hosts.
30 minThis is one of the most disgraceful pieces of play-acting I have ever seen. Santander goes down clutching his face in the penalty area but Huth has only held onto his shoulder. He stays down and the ball is kicked out. So poor.
33 minSHOT! Vardy goes for the worldie volley after a Copenhagen heads the ball into the air but he doesn't catch it cleanly and it rolls through to Olsen.
35 minVardy is normally known for the shift he puts in but it's Slimani who is chasing everything down for the Foxes. He's been far and away Leicester's best player but that's not really saying much tonight.
39 minVardy makes a clever run into the left channel and he earns a free kick after getting across the defender. Fuchs's delivery is solid enough but Olsen is able to punch clear.
40 minGOAL! Leicester City 1-0 Copenhagen (Mahrez)
40 minLeicester break the deadlock! I was just about to say that Leicester are over-reliant on the high ball towards the box but it's the height of Slimani which proves important here. Vardy's cross is headed back across goal by the Algerian for fellow countryman Mahrez, who flicks the ball into the net from six yards.
44 minCHANCE! The home side need to do all they can to ensure they go into the break with the advantage but Copenhagen are coming straight back at them. Toutouh has just seen a long-range effort deflected over the crossbar before Cornelius got ahead of Huth and glanced a header wide of the post.
8.33pmThe half-time whistle goes at the King Power Stadium and Leicester take a 1-0 lead into the break thanks to Mahrez's clever finish. Chances have been few and far between but Leicester won't care - they are 45 minutes away from a third successive victory in the Champions League.
46 minLeicester get us back underway. No changes at the break.
46 minSHOT! Much better from Leicester as Vardy creates an opportunity for Mahrez to whip a first-time shot into the top corner but he gets it all wrong and it goes into the stand. He was scoring those type of chances last season.
49 minMorgan still doesn't look right. The problems are coming when he has to turn sharply or get back off the ground. It's something to keep an eye on.
52 minLeicester must have had a talking to at the break because they look a different team at the start of this half. It's now where they need to take full advantage and find a second goal because that would likely be enough for victory.
54 minIt's worth noting that Club Brugge are still beating Porto. If the Belgians can hold on there and Leicester can win here, the Foxes would be five points clear at the top of the group. I will stop getting ahead of myself, though...
56 minCHANCE! The visitors are always a danger from set pieces and after they just miss out on making connection with a corner, the ball is fired back in and Cornelius's flick is too close to Schmeichel.
60 minLeicester look threatening on the break but Copenhagen have had the better of the last five minutes. They need to stay tight before the first wave of substitutions start. Don't be surprised to see Amartey come on.
64 minCHANCE! A long ball from Schmeichel causes all kinds of problems for the Copenhagen defence but after Mahrez picks up the ball and glides past a couple of defenders, his final shot is poor and blocked.
67 minLeicester have the ball in the back of the net as Slimani finds the back of the net at the second time of asking. However, he is ruled offside and it appears to be the wrong decision. The forward was level with the defender at the time of Albrighton's cross. Could that be a game-changer?
70 minIt has to be said, that was a very poor decision. The assistant was level with the play. Ranieri doesn't get angry very often but he will if Leicester don't win this game.
73 minThere's been another goal in Belgium and Porto have equalised against Club Brugge. A draw would still be a good result for both Leicester and Copenhagen but you'd expect Porto to be pushing for a winner.
76 minWe have less than 15 minutes remaining and we are still awaiting Leicester's first substitution, which is a bit of a surprise. Ranieri has players on the bench that could impact this game.
79 minBOOKING! The first booking of the night goes to Fuchs for a foul on the halfway line. Looked a bit harsh.
81 minAs we enter the final 10 minutes, it's Copenhagen who look most likely to find a goal. Falk does excellently to win a corner for his side but the resulting set piece only finds the first man.
83 minSHOT! Falk has been extremely lively since his introduction earlier in this half and he manages to set up Kvist. However, the former Fulham and Wigan man can only shoot into the hands of Schmeichel from 20 yards.
86 minSUBSTITUTIONS! Ranieri finally makes his first change with Okazaki replacing Vardy. Copenhagen have also made a couple of alterations as they look to throw the kitchen sink at the Foxes.
87 minCHANCE! Big chance for Copenhagen! A cross is hung up at the back post for Santander but his header - which appears to be goalbound - is deflected over by Simpson. It was a very timely intervention.
88 minSUBSTITUTION! Another substitution for Leicester and Slimani - who has probably been the home side's best player - makes way for Ulloa.
90 minSAVE! What a save from Schmeichel! He has not had a lot to do but he has just pulled off a wonder save to deny Cornelius from eight yards. He flung out a hand and it was enough to stop the former Cardiff City man from finding the bottom corner.
90+2 minThere will be three minutes of added-on time.
9.42pmThe full-time whistle goes at the King Power Stadium and Leicester have held on for what could be a priceless win! They were indebted to Schmeichel's save at the end but it's Mahrez's goal which have proven to be the difference this evening.
9.42pmPorto scored a late, late winner at Club Brugge to take some of the shine off the evening but right now, Leicester won't care. They are five points clear at the top of Group G.
9.43pmThat will be all from Sports Mole for this game. Thank you for joining us and we hope to see you again tomorrow evening when the likes of Manchester City, Barcelona, Arsenal and Celtic are all in action. Goodbye for now.