Manchester United also made it three wins out of three with a 1-0 victory at Benfica, as did Barcelona, which beat Olympiakos 3-1, despite playing the entire second half with 10 men. Elsewhere, Atletico Madrid looks to be heading for an early exit after drawing 0-0 at Qarabag. Basel won 2-0 at CSKA Moscow.
Here's a closer look at the four groups:
Manchester United took advantage of an embarrassing mistake by the youngest goalkeeper ever to play in the Champions League to beat Benfica 1-0 and maintain its Group A lead.
Belgian goalkeeper Mile Svilar, making his Champions League debut at age 18, was deceived by a long free kick taken by Marcus Rashford in the second half, going over the line while holding the ball with his arms outstretched in front of him.
He misjudged Rashford's shot and couldn't stop his momentum after stepping back toward the goal to make the catch. The ball just crossed the line and the referee confirmed the strike with the help of goal-line technology.
Manchester United reached nine points with its third straight win in Group A. It has a three-point lead over Basel. CSKA stayed with three points, while Benfica has zero points after three losses.
PSG continues to go from strength to strength in the Champions League and it currently sits atop Group B with 12 goals for, none against and three victories.
Kylian Mbappe scored after less than three minutes before setting up Edinson Cavani for a close-range header shortly before halftime.
The world's most expensive player, Neymar, also had his moment in the second half — sending a low free kick under the soaring defenders and past goalkeeper Matz Sels in the 66th minute. Angel Di Maria rounded off the scoring two minutes from time.
Bayern remained three points behind PSG after a comfortable win in Jupp Heynckes' second match in charge, and moved three points above Celtic. Anderlecht is still without a point.
Heynckes, who retired after guiding Bayern to the Champions League, Bundesliga and German Cup treble in 2013, has the German powerhouse running smoothly again after taking over from Carlo Ancelotti, who was fired after the side's 3-0 defeat at PSG.
Thomas Mueller and Joshua Kimmich put Bayern 2-0 up inside half an hour and Mats Hummels wrapped it up when he headed in a corner shortly after the break.
Cheslea salvaged a point against Roma when Eden Hazard headed in his second goal of the night in the 75th minute.
Edin Dzeko's double had briefly put Roma in front but 2012 Champions League winner Chelsea remains two points ahead of the Italian club at the top of the group.
Chelsea had made a blistering start at Stamford Bridge with David Luiz curling a shot into the bottom corner after 11 minutes.
Hazard doubled the Premier League champions' lead but Aleksandar Kolarov pulled one back for Roma five minutes before halftime.
Atletico Madrid is three points behind Roma after being held 0-0 by newcomer Qarabag, which earned its first point in its third game.
The match was marked by the disputed dismissal of Qarabag forward Dino Ndlovu, who was judged to have dived in the 75th minute, drawing his second yellow card of the night.
Lionel Messi scored his 100th goal in European competition when he curled a free kick over the wall in the 61st minute. Olympiakos goalkeeper Silvio Proto got a hand on the ball but couldn't keep it out as Messi took his career tally in the Champions League to 97 goals.
Messi also set up left back Lucas Digne to score in the 64th when he dribbled around a defender before cutting the ball back through the area for his teammate to drive it home.
Nikolaou scored Olympiakos' consolation goal with a header from a corner in the 90th.
Barcelona had gone ahead thanks to an own-goal by Dimitris Nikolaou in the 18th, but the hosts were left a man down three minutes before halftime. Gerard Pique got a second booking for using his arm to steer the ball into the net. The strike was disallowed.
Barcelona remained three points ahead of Juventus, with Sporting three points further back. Olympiakos has zero points.
Mario Mandzukic scored the winner for the Italian side six minutes from time after free-kick specialist Miralem Pjanic had canceled out an own-goal by Juventus defender Alex Sandro in the first half.