Manchester City face a huge task to qualify for the knockout round of the Champions League after a home loss to CSKA Moscow, while Chelsea failed to overcome Maribor as Matchday 4 concluded on Wednesday.
The visitors, who battled back to draw 2-2 with City in Moscow, found themselves ahead after just two minutes at the Etihad Stadium as Seydou Doumbia headed home, but the lead lasted little over five minutes as Yaya Toure powered in a free kick.
However, CSKA continued to carry a threat, and when Gael Clichy gave away possession to Bebars Natcho, he played in Doumbia for his second of the night.
City's plight worsened when Fernandinho was dismissed for a second bookable offence on 70 minutes, and Toure then followed him into the changing room with nine minutes to play when he was shown a straight red card for shoving Roman Eremenko.
Sergio Aguero was then shown a yellow card for simulation in the area to complete a dismal night for Manuel Pellegrini's men.
Bayern Munich have secured top place in the group after they maintained their 100 percent record with a 2-0 victory over Roma.
Roma were looking to bounce back from their 7-1 humiliation at their home ground, but they were powerless to prevent Franck Ribery slotting the ball expertly home after David Alaba's rapid counter.
Robert Lewandowski then made space down the left to produce a cross for former Borussia Dortmund teammate Mario Gotze to divert home.
The Blues had emerged 6-0 winners in the game at Stamford Bridge, but Maribor appeared much more threatening on their home ground. There were chances for both sides in the first half, and Jose Mourinho moved to bring on both Diego Costa and Oscar at the break in an attempt to spark an improvement.
However, the hosts took a shock lead fives minutes into the second half when Agim Ibraimi curled a wonderful shot past Petr Cech. They should have doubled their lead as the game approached the hour mark, but Luka Zahovic somehow fired over the bar with the goal at his mercy.
Chelsea then saw a penalty turned down as Oscar appeared to draw a foul in the box, but an equaliser followed soon afterwards as Nemanja Matic turned the ball home at the far post.
Diego Costa then saw a goal controversially ruled out for offside, and Eden Hazard then failed from the spot after having won his side a penalty.
In the same group, Sporting won an entertaining match 4-2 against Schalke.
An Islam Slimani own goal had the Bundesliga side ahead of 17 minutes, but Mahamadou-Naby Sarr headed home an equaliser on 26 minutes before fellow defender Jefferson gave the Lisbon side the lead with 52 minutes gone.
Sporting then extended their advantage when Nani turned in a cross and, though Schalke replied with a fine Dennis Aogo goal. Slimani raced clear to make sure of the result in injury time.
Barca made the breakthrough on 36 minutes when Ajax keeper Jasper Cillessen failed to deal with a ball on the edge of his box, allowing Marc Bartra to take possession and hook a cross back for Lionel Messi to head home.
Ajax's hopes took a major blow when Joel Veltman picked up a second yellow card, and Messi then scored his second of the night -- taking him level among the competition's all-time leading scorers -- as he exchanged passes with Pedro before diverting home.
Paris Saint-Germain remain in control of the group, though, after they saw off APOEL Nicosia 1-0.
PSG were ahead within a minute, Edinson Cavani firing home a Gregory van der Wiel cross, and that proved enough to take three points and keep them in top spot.
After eliminating Napoli to reach the group stages, Athletic have struggled to impress, entering this match with only one point from their previous three games.
Porto might have been ahead just before the break when Mikel Balenziaga fouled Danilo in the area, but Jackson Martinez hit the bar with the ensuing spot kick.
The Colombian was able to make amends in the second half, though, as he bundled home Yacine Brahimi's cross, and Brahimi then got his own name on the scoresheet after a terrible goalkeeper error.
Shakhtar Donetsk eased to a 5-0 victory over BATE Borisov as Luiz Adriano fired a hat trick.
Darijo Srna fired Shakhtar ahead after 19 minutes when his low shot was deflected home, and they were two up shortly after the break when defensive confusion allowed Alex Teixeira to prod home.
Adriano then added a further three goals, the first from the penalty spot, to wrap up the win.