Soon after the break, they doubled their advantage through Emanuele Giaccherini and Bayern were not able to respond as they ended their home tournament without scoring a goal.
Read below to see how the game unfolded at the Allianz Arena.
4.16pmHello, and welcome to Sports Mole's live coverage of the third-place playoff in the Audi Cup between Bayern Munich and Napoli.
4.21pmIt's not often that Bayern Munich are forced to contest a third-place playoff - especially at their home ground - but that is what is in front of them today. After yesterday's humbling by Liverpool, they have missed out on featuring in the final of the competition at the Allianz Arena and they now must attempt to salvage some pride with what is effectively a meaningless fixture against Napoli. It's a similar situation for the Italians, who let slip a one-goal lead against Atletico Madrid.
4.23pmWe have only got just over 20 minutes until kickoff so for once, we won't hang about in bringing you the two teams. First up, Bayern...
4.24pmBAYERN MUNICH XI: Fruchtl, Sule, Rudy, Vidal, Coman, Kimmich, Tillman, Friedl, Sanches, Mai, Wintzheimer
4.26pmNAPOLI XI: Sepe, Maggio, Maksimovic, Koulibaly, Ghoulam, Zielinski, Diawara, Hamsik, Callejon, Mertens, Insigne
4.31pmAs expected, Bayern boss Carlo Ancelotti makes mass changes to his side given the short recovery period after yesterday's semi-final. Niklas Sule, Sebastian Rudy, Arturo Vidal, Kingsley Coman and Renato Sanches are the players involved who can be deemed first-team players, with the remainder of the side all looking to make an impression. Seventeen-year-old Christian Fruchtl takes his place between the sticks.
4.35pmAs for Napoli, Maurizio Sarri names a stronger team than perhaps many expected. The majority of the players which have been included have claims to feature in the starting lineup on a regular basis and on paper, they should probably be regarded as favourites to win this match. Piotr Zielinski features in midfield - he has been linked with Liverpool since the end of last season so it would not come as a surprise if Jurgen Klopp is keeping an eye on his performance.
4.38pmBefore the two teams make their way out at the Allianz Arena, a quick reminder that straight after this game, we will have full coverage of Liverpool's showdown with Atletico Madrid. The Merseyside giants will be without Daniel Sturridge, but they may come up against one of their legendary strikers in Fernando Torres.
4.42pmYesterday, we had torrential rain in Munich but today, it's bright sunshine! Many of the supporters are fanning themselves in an attempt to cool down. Maybe the conditions will have an impact on the pace in which this game is played at.
4.47pmWell we have reached the scheduled kickoff time and the players are only just emerging from the tunnel. We are running about five minutes late. Don't believe all you hear about German efficiency.
1 minBayern get us underway.
3 minThere's not a lot happening at the moment. Both teams are looking to play the ball about, but there doesn't appear to be that much urgency. Fruchtl has had a few early touches in the Bayern goal.
7 minSHOT! Bit better from Bayern, who are now trying to force the issue and exchange passes in the Napoli half. A long spell of possesses ends with Coman getting a well-struck shot away from around 16 yards out, but Sepe is equal to it.
9 minThis is an excellent tackle from Maggio. A searching ball finds Tillman but just as he is about to shoot from the edge of the penalty area, the right-back gets across to make the challenge.
11 minCHANCE! Ancelotti must have read the riot act to yesterday's team but this completely different side is playing some superb stuff. Another neat move almost ends with success as Kimmich makes his way into the penalty area but his low drive from a tight angle is well blocked by Sepe.
13 minCHANCE! Another opportunity for Bayern. The ball finds Vidal at the back post but after he cuts back onto his right foot, his effort from about 12 yards is straight at Sepe.
14 minGOAL! Bayern Munich 0-1 Napoli (Koulibaly)
14 minAgainst the run of play, Napoli take the lead. A free kick swung into the middle finds Maksimovic, who sees a close-range effort saved by Fruchtl. However, the rebound falls to Koulibaly and he can't miss from inside the six-yard box.
18 minIn all fairness to Bayern, they have reacted well to going behind. They have picked up where they left off in the Napoli half but they are yet to create another opening since the goal.
24 minCHANCE! Not much else to report over the past five minutes but Mertens almost doubles Napoli's lead after breaking clear of the Bayern defence, but Fruchtl stayed big to make an important block. The youngster is performing well so far. He certainly doesn't look out of place.
30 minDespite the increased heat in Germany, this is being played at quite a lively pace. Bayern are still the better side, but they do look susceptible on the break. Mertens and Insigne are causing them plenty of problems.
34 minBayern win a free kick on the left flank and Friedl is the man given responsibility to whip in the cross. It's a decent delivery but Napoli defend it well.
37 minSHOT! Sanches - a player who is being linked with a number of top European clubs at the moment - tries his luck from distance but his strike takes a nick off a defender and just goes past the post.
42 minWe are nearing the end of the first half and while we remain at 1-0 to Napoli, it's Bayern who will consider themselves to have played the better football. Ancelotti is likely to keep with this team when they return given that he made 11 alterations from yesterday, but expect Sarri to make changes to his Napoli team.
45 minHALF TIME: Bayern Munich 0-1 Napoli
5.36pmThe half-time whistle goes in Munich and Bayern trail thanks to that early goal from Koulibaly. The German giants will count themselves unfortunate to be behind but Napoili have arguably created the more clear-cut opportunities.
46 minWe are back underway. Changes have been made but I will bring you up-to-date as we progress.
47 minFrom what we can see, Cabral and Rui have been introduced by Napoli, with Ghoulam one of the players to be withdrawn.
50 minWe haven't seen much of Wintzheimer in the Bayern attack but Tillman continues to look impressive. He has generally had the better of the experienced Maggio without supplying an end product.
51 minSHOT! That same player, Tillman, was just presented with a chance on the left side of the penalty area but his low drive was straight at Cabral.
55 minGOAL! Bayern Munich 0-2 Napoli (Giaccherini)
55 minNapoli double their advantage through Sunderland reject Giaccherini. Mertens does well in getting towards the byline before pulling the ball back for his teammate, who takes a touch before lashing a shot into the bottom corner.
58 minSHOT! There are a few signs of desperation in the Bayern side. Vidal takes a shot from at least 30 yards but it is always rising and ends up in the stand.
61 minSUBSTITUTIONS! Plenty more changes from Napoli. Jorginho and Chiriches are among the newcomers.
64 minSUBSTITUTIONS! It is now the turn of Bayern, with Tolisso and Ribery among those who have been introduced.
68 minThose substitutions have disrupted the rhythm of play and although Napoli are shading the action, it's very stop-start. The Italian side have looked good this evening. It is acting as perfect preparation for their Champions League qualifying tie, which will take place later this month.
73 minBOOKING! I'm not so sure we are going to have too many more chances in this game. Sharpness has definitely been lost with both teams. However, we have had a booking, with Jorginho being cautioned for his follow-through after winning the ball.
74 minBOOKING! Mertens follows him with a needless trip on Rudy. The Bayern player is not amused.
78 minWe haven't seen much of Ribery since he was introduced but a direct run down the left results in a corner being won. Unfortunately for Bayern, nothing comes from it.
82 minSHOT! We have finally had another shot on goal, with Milik looking to get in on the action from a free kick. However, despite his shot being well struck, it curled just wide of the post.
86 minBayern are looking to mount one final charge on goal but Napoli are well stocked for numbers at the back. Former Spurs centre-back Chiriches has performed well since coming on.
90 minFULL TIME: Bayern Munich 0-2 Napoli
6.40pmThe full-time whistle goes at the Allianz Arena and Napoli have comfortably held on to claim a 2-0 win over Bayern, who end the Audi Cup without scoring a goal. They entered their home tournament as the favourites, so this will go down as a significant setback for Carlo Ancelotti.
6.41pmThat will be all from Sports Mole for this match. Thank you for joining us for this game and we hope that you can return for coverage of Liverpool's showdown with Atletico Madrid, which starts at 7pm, BST. Goodbye for now.