There was no repeat of the defending champions' 5-0 thumping of the Czech side in Munich a fortnight ago as Mario Mandzukic netted the only goal of the game with a 65th-minute header to maintain his side's 100 per cent record.
As a result of the victory, Bayern equalled the most consecutive wins ever recorded in the Champions League, with the tally now at nine after winning the trophy last season.
Following a 7-0 Barclays Premier League thrashing of Norwich at the Etihad Stadium on Saturday, City were again in the goals on home soil as they recorded a 5-2 victory over CSKA Moscow.
That result, combined with Bayern's success over Plzen, means City are already through to the last 16.
A Sergio Aguero penalty, after David Silva had been fouled by Zoran Tosic, gave City the lead inside three minutes, with the Argentinian doubling his tally for the night in the 20th minute with a right-foot drive for his 13th goal of the season.
Alvaro Negredo then followed up with a hat trick with goals in the 30th, 51st and 90th minutes, with City's march to victory briefly tempered by goals from Seydou Doumbia in the 45th and 71st minutes, the latter from the spot.
Real Madrid and Paris St Germain both have one foot in the door of the last 16 after they were held to 2-2 and 1-1 draws against Juventus and Anderlecht respectively to end their own hopes of winning every game in the group stages.
At the Juventus Stadium, the Italian side grabbed the lead against Real via a 42nd-minute penalty from Arturo Vidal before Ronaldo and Gareth Bale struck in eight second-half minutes by the hour mark to edge the La Liga side in front.
Fernando Llorentes, however, rescued a point for Juve to leave Real needing only a draw from their remaining two Group B games to guarantee their passage into the knockout phase.
Demy de Zeeuw fired the visitors in front in the 68th minute, only for Zlatan Ibrahimovic to haul the hosts level two minutes later.
That was prior to Anderlecht finishing the game with 10 men after Sacha Kljestan was dismissed in the 82nd minute for a second bookable offence.
In Group A both games finished goalless, leaving Manchester United and Bayer Leverkusen as the teams still favourites to qualify.
United will be without Marouane Fellaini for the next game in Leverkusen on November 27, however, after the midfielder was dismissed for a second bookable offence in the 90th minute.