Leverkusen paid the ultimate price for their poor finishing on the hour mark when Joao Moutinho scored the only goal of the game.
Find out how all of the action unfolded with our minute-by-minute text commentary below.
6.55pmGood evening and welcome to our live coverage of the Champions League group stage match between Monaco and Bayer Leverkusen, two teams that have experienced contrasting fortunes domestically this season.
6.57pmMonaco are here tonight by virtue of finishing second in Ligue 1 last season, behind Paris Saint-Germain. This is a big night for Leonardo Jardim's side, marking their first European outing since 2006.
7.00pmJardim's men have not gotten off to the ideal start to the new campaign, picking up just four points from their first five league matches and losing the talismanic Radamel Falcao to Manchester United. They lost 2-1 to Lyon on Friday, their third reverse of the season.
7.04pmLeverkusen are no strangers to European football in recent seasons. They reached the last 16 of this competition last term and were knocked out by French opposition in the form of PSG.
7.06pmRoger Schmidt's side have been quick off the starting blocks in the Bundesliga and currently occupy the top spot in the league table, with a pair of wins and a draw so far. They dropped their first points of the season on Friday when Werder Bremen held them to a 3-3 draw at home.
7.10pmIt's a big night for Dimitar Berbatov, who faces one of his former clubs this evening. The big Bulgarian featured more than 150 times for Leverkusen and scored 69 goals during that time, before departing for Tottenham Hotspur.
7.15pmTeam news coming up...
7.16pmMONACO XI: Subasic, Fabinho, Kurzawa, Carvalho, Raggi, Moutinho, Kondogbia, Toulalan, Berbatov, Ocampos, Ferreira-Carrasco
7.16pmLEVERKUSEN XI: Leno, Spahic, Jedvaj, Boenisch, Toprak, Bender, Hakan Calhanoglu, Castro, Bellarabi, Son Heung-Min, Kiessling
7.19pmMonaco look like they are going for it tonight, lining up with a 4-3-3 formation, with Lucas Ocampos and Yannick Ferreira Carrasco taking on advanced midfield roles to partner Berbatov in the attack.
7.21pmStefan Kiessling will operate as a lone striker for the visitors, as Schmidt as chosen to pack the midfield. Among that midfield is Lars Bender, who makes his first start for four months following a thigh injury.
7.27pmThere's just over 15 minutes to go until kickoff, but we have some pre-match quotes from both managers for you before then.
7.28pmRoger Schmidt: "We are confident and the players know it. We have analysed Monaco's game and they are a good team. They have not played in Europe for a while but they are not outsiders. It is only early in the season, the standings do not mean anything. Monaco have a lot of quality and the UEFA Champions League is a different competition, so we cannot compare it with the league."
7.31pmLeonardo Jardim: "The UEFA Champions League is a very important competition - a lot is at stake. And usually results hinge on small details. Leverkusen are strong and very quick on the break. We will have to be careful from set pieces. We will have to raise our game and be efficient up front. The youth of our team is not an issue. We need to find a bridge between the current situation and the future that is in front of us - which is very promising."
7.32pmPREDICTION: I think Leverkusen will fancy their chances tonight and come out on top. They have a lot of European pedigree, while Monaco haven't played in this competition for some time. I'm expecting them to come away with a 2-1 win.
7.37pmIn tonight's other Group C match, Benfica play host to Zenit St Petersburg. You can follow our live coverage of that game here.
7.39pmLeverkusen and Monaco are the favourites for first and second in this group, so the result of this evening's match could go a long way to deciding which one of them takes the top spot.
7.40pmThe two teams are heading out onto the pitch now. It's a disappointing turnout tonight, with empty seats across the stadium. The atmosphere isn't what Monaco were hoping for on an evening that marks their long-awaited return to Europe.
1 minKICKOFF The visitors get the match under way, kicking from left to right in the first half. They immediately look to be imposing, but the early attack breaks down as they concede a free kick deep in Monaco's half.
3 minThere's an early penalty shout from Yannick-Ferreira Carrasco, who goes tumbling in the Leverkusen area, but the referee isn't interested. In all fairness, he made a meal of the challenge.
7 minMonaco have passed the ball around incisively in these early stages, but their opponents are dispossessing them too easily. They have just been awarded a free kick in the danger zone, which was played to the feet of Yannick Ferreira Carrasco, who blazed the ball over from long range. Wasteful from him!
10 minThe French side have settled into the game better than their opponents and look threatening along that left flank, with Layvin Kurzawa making some good runs. He almost played in Dimitar Berbatov, but the Bulgarian was caught offside.
14 minsCHANCE! Gonzalo Castro misses a sitter for the visitors following a deadly counter-attack. Hakan Calhanoglu picked him out with a cross-field pass, but the midfielder put his effort wide despite having a clear sight of goal. The Monaco defence were caught napping there!
16 minCHANCE! Another opportunity falls Leverkusen's way as Hakan Calhanoglu fires into the sidenetting following good work by Stefan Kiessling. The Germans are in the ascendency now, but neither side has hit the target so far.
19 minLeverkusen threaten from a free kick after Lucas Ocampos commits a foul. It's played high to Omer Toprak, who puts a free header over the crossbar. Monaco win a free kick of their own in their opponents' half moments later following a handball. Joao Moutinho provides a decent delivery, but his teammates were too poorly positioned in the area to capitalise.
23 minThere's a half-chance for Monaco following yet another set piece, which Moutinho takes quickly. Fabinho lays it on to Ferreira-Carrasco, whose effort flies well over the bar. Neither goalkeeper has been tested yet.
26 minBOOKING! Yannick Ferreira-Carrasco receives the first yellow card of the game for what can only be described as a cynical challenge on Emir Spahic. He can have no complaints about that booking. The Leverkusen defender is still on the deck.
29 minLeverkusen are looking the more capable footballing side now, despite Monaco having some decent spells earlier on. The Ligue 1 side's midfield trio are failing to hold off the opposition's counter-attacks, making it easy for them to get going.
31 minFerreira-Carrasco with a flurry there, beating two Leverkusen players along the right flank, but he fails to get his pass off. Play is stopped moments later as Castro handballs in the middle of the park to gift Monaco a free kick.
36 minABSOLUTE SITTER! Leverkusen should be in the lead, no question! Karim Bellarabi goes clean through on goal as Calhanoglu picks him out with a cheeky ball over the top. He's one-on-one with Danijel Subasic, but doesn't even test the Monaco keeper, spraying his effort wide!
39 minFerreira-Carrasco plays a decent ball into the Leverkusen box, but there were no red shirts in there to take advantage of it. Dimitar Berbatov is having a hard time playing up front on his own, but he was nowhere to be seen then!
42 minMonaco's defensive pairing of Andrea Raggi and Ricardo Carvalho have been poor this evening, lacking pace and power, and failing to deal with those high balls. I'm not sure how much longer they are going to hold out.
44 minANOTHER MISS! The visitors should be out of sight already. Heung-Min Son is the latest Leverkusen player guilty of a glaring miss as Gonzalo Castro picks him out unmarked in the penalty area. The South Korean drags his shot wide, once again failing to test Subasic.
45 minThere will be two minutes of stoppage time in the first half.
45+2 minThere is time for Leverkusen to squander another goalscoring opportunity before the half-time whistle blows as a Castro volley is deflected behind off Kurzawa, but that's it for the first period.
45+2 minHALF TIME: Monaco 0-0 Bayer Leverkusen
8.37pmHow on earth this this game goalless? Leverkusen must be wondering how they aren't two are three goals up at the break. Neither goalkeeper has really been tested, but all of the best chances have fallen the way of the Germans.
8.39pmGonzalo Castro, Karim Bellarabi and Heung-Min Son all failed to convert golden opportunities as Monaco's defensive pairing of Andrea Raggi and Ricardo Carvalho looked out of their depth in the Champions League.
8.42pmIf you've just joined us, you can catch up with all of the action from the first half with our half-time report here.
8.45pmIn tonight's other group C match, Zenit are 2-0 up against 10-man Benfica. You can get yourself up to speed on that one here.
8.47pmBoth sets of players are heading back out onto the pitch now. Stick with us for minute-by-minute updates from the second half!
46 minKICK OFF: Monaco get the second period under way and immediately hand Leverkusen a free kick with a foul on Son Heung-Min. Calhanoglu plays a lofted pass to the centre of the box but Subasic races off his line and claims it.
48 minCalhanoglu races along the right wing, cuts inside the area and play a swift pass across the face of goal, which Andrea Raggi does well to turn behind for a corner.
50 minMonaco apply some pressure of their own in the final third as Ferreira-Carrasco plays a dangerous ball into the box. Once again, there is nobody there to claim it, which allows the Germans to regain possession. Their attempt to counter breaks down as Kurzawa fouls Kiessling.
54 minThe hosts show just what they are capable of on a good day as Kondogbia, Moutinho and Kurzawa combine beautifully to win a free kick in a good position, but the resulting ball is claimed easily enough by Bernd Leno in the away goal.
56 minBENFICA SUB: Bernardo Silva replaces Lucas Ocampos as Monaco attempt to add some solidarity to their midfield. That is where they appear to be losing this battle.
58 minMonaco are in the midst of their best spell of the game and Layvin Kurzawa has been involved in everything they have created. The wing-back wins a corner as Tin Jedvaj turns his cross behind.
60 minGOAL! Monaco 1-0 Bayer Leverkusen (Joao Moutinho)
60 minKurzawa makes a lovely run that spans most of the pitch before picked out Berbatov. The Bulgarian plays in Moutinho with a headed pass, and the midfielder does the rest, rifling one into the top corner from inside the box.
62 minMonaco's goal was against the run of play overall, but they have dominated the last 10 minutes. Kurzawa plays another good ball into the box looking for Berbatov, but Bernd Leno beats the striker to the cross.
65 minLEVERKUSEN SUB: Giulio Donati replaces Tin Jedvaj in a like-for-like switch at the back. Not the change I was expecting from the visitors.
67 minJedvaj must have been carrying some kind of injury as Reinartz is not a natural centre-back. The visitors' back line is now looking somewhat makeshift.
70 minThat goal has given the hosts a confidence boost and knocked the stuffing out of Leverkusen, who were utterly dominant in the first period but can't seem to get a foothold in the match at the moment.
75 minLEVERKUSEN SUB: Drmic replaces Lars Bender as the visitors make a very attacking change, throwing on a striker for a defensive midfielder. Will that be enough to salvage something from this match?
77 minIt's still Monaco in the ascendency. They look like a rejuvenated side at the moment, chasing lost causes and striking terror into the hearts of the visitors' three-man defence with their pace.
78 minThere's a nervy moment for Danijel Subasic in the Monaco goal as he almost allows a tame effort from Bellarabi to allude him and creep into net. Incredibly, that was Leverkusen's only shot on target this evening.
81 minCHANCE! A great chance for Monaco to put the game to bed goes begging as Ferreira-Carrasco links up with Berbatov and goes clean through on goal, but Bernd Leno races off his line and steals the ball away from the Belgian at the last second.
85 minCHANCE! A chance falls to Leverkusen at the other end of the park as Stefan Kiessling rises high to meet a free kick, but his header is comfortably saved by Danijel Subasic.
90 minThe fourth official reveals that there will be four minutes of stoppage time to play.
90+4 minFULL TIME: Monaco 1-0 Bayer Leverkusen
9.39pmBayer Leverkusen looked utterly spent by the end as Monaco edge their noses over the finish line. The Germans paid the ultimate price for their poor finishing in the first half and leave France empty-handed.
9.41pmMonaco get their first European campaign in almost a decade off to a winning start, a result that could kickstart their domestic season.
9.44pmThat's all we have time for here, but stick with Sports Mole for match analysis, player ratings and reactions from all of this evening's Champions League fixtures.