Barcelona, spurred by Lionel Messi's 100th European goal, Manchester United and Paris St Germain maintained perfect records, while Chelsea and Roma were involved in a six-goal draw.
Bayern Munich eased past Celtic to hand coach Jupp Heynckes a victorious return to the competition he won with them in 2013 and Juventus hit back to snatch a late 2-1 win at home to Sporting after gifting the Portuguese side an early lead with a bizarre own goal.
A summary of Wednesday's group matches in the UEFA Champions League.
Messi joins 100-goal club in Europe as Barca cruise
Lionel Messi scored his 100th goal in European competition as Barcelona moved close to qualifying for the Champions League knock-out stages after outclassing Olympiakos 3-1 on Wednesday despite playing the second half with 10 men.
Gerard Pique was sent off two minutes before half-time for two bookings, one for tugging an opponent's shirt and the other for slapping the ball into the net, but Barca were barely threatened by a hapless Olympiakos side who are badly under-performing in their Greek title defence.
The Athens club, who won three league titles and two domestic Cups under current Barca coach Ernesto Valverde, are fifth in the standings in the Greek top flight and have lost all their games in the Champions League.
Barca took the lead in the 18th minute at a rainswept and sparsely attended Nou Camp when visiting defender Dimitrios Nikolaou turned Gerard Deulofeu's cross into his own net.
It was the fifth own goal Barca have benefited from this season in all competitions.
Messi struck his landmark goal in Europe from a free-kick in the 61st minute to double Barca's lead. It was his 97th goal in the Champions League. His other three came in the UEFA Super Cup.
Messi then carved his way through the hapless visiting defence moments later to tee up France left back Lucas Digne to score his first goal in the Champions League for Barca.
Greek defender Nikolaou, 19, scored for a second time but first for his side when he headed home from a corner to give Olympiakos a scantly-deserved consolation goal in the 89th minute.
The unbeaten Barca top Champions League Group D with nine points. A win at Olympiakos in two weeks will seal their place in the last 16.
Rookie keeper's howler gifts Manchester United win at Benfica
An embarrassing mistake by Benfica's 18-year-old goalkeeper Mile Svilar gifted Manchester United a 1-0 win at Benfica in Group A.
The 18-year old Belgian, the youngest keeper to play in the Champions League, was undone by Marcus Rashford's long-range free-kick in the 64th minute, catching the ball before back-pedalling and carrying it behind the goalline with his arms outstretched.
After breaking into tears at the final whistle, the son of former Serbian goalkeeper Ratko Svilar was consoled by United striker Romelu Lukaku, whose quiet evening underlined the English club's toothless performance.
The display was almost a carbon copy of Saturday's 0-0 Premier League draw at Liverpool but it extended their unbeaten run in both competitions this season under manager Jose Mourinho and left them top of the section with a maximum nine points.
Swiss side Basel are second with six points after a 2-0 win at CSKA Moscow, three points ahead of the Russian team, while Benfica are bottom with none.
Benfica were reduced to 10 men in stoppage time when defender Luisao was sent off after receiving his second yellow card.
Chelsea, Roma share spoils in thriller
Chelsea and AS Roma served up a rip-roaring 3-3 draw at Stamford Bridge as both clubs stayed firmly on course for a place in the last 16 of the Champions League.
An enthralling contest saw Edin Dzeko score twice as Roma stormed back from 2-0 down to lead 3-2 with 20 minutes remaining, only for Eden Hazard to salvage a point for Group C leaders Chelsea with a rare header.
The goal flow began in the 11th minute when David Luiz's curler put Chelsea ahead and when Hazard doubled the home side's advantage in the 35th it looked like being a routine night for Antonio Conte's side.
Aleksandar Kolarov fired Roma back into contention before the interval though and Dzeko's double in the space of six minutes, the first a scorching volley, looked to have earned Roma only their second win in 16 attempts on English soil.
Hazard's equaliser kept Chelsea top with seven points from three games with Roma on five -- three ahead of Atletico Madrid who were surprisingly held to a 0-0 draw by Qarabag.
Terrific trio on target as PSG thump Anderlecht
Paris St Germain’s feared attacking trio all got on the scoresheet as the French side completed a comfortable 4-0 away victory over Anderlecht in their Champions League Group B clash.
Kylian Mbappe, Edinson Cavani and Neymar, who form the world’s most expensive frontline, all netted, while Angel Di Maria added a fourth with a late strike, in a win that maintains the Ligue 1 side’s 100 percent record in the group stage with three wins from three.
They head the standings with nine points from second-placed Bayern Munich, who have six. Celtic are in third with a single victory to their name, while Anderlecht are still searching for their first points.
PSG should have won by a greater margin as they spurned a number of chances and will be confident of victory when the teams meet again in their next fixture in the group in Paris on October 31.
Juve recover from bizarre own goal to snatch late win
Juventus hit back to snatch a late 2-1 win at home to Sporting after gifting the Portuguese side an early lead with a bizarre own goal by Alex Sandro.
Four days after their two-year unbeaten home run was ended by Lazio, Juve were in more trouble when goalkeeper Gianluigi Buffon saved at the foot of Gelson Martins but the ball hit Alex Sandro and went straight into the net.
Miralem Pjanic levelled with a superb free-kick in the 29th minute and, just as Sporting seemed set to frustrate the hosts, Mario Mandzukic scored the winner with a superb diving header in the 84th minute.
Juventus have six points from three games in Group D, three behind leaders Barcelona, while Sporting are on three.
Already fending off talk of a crisis after taking one point from their last two league games, Juventus got the worse possible start with a double mistake by Alex Sandro in the 12th minute.
The Brazilian first failed to cut out Bruno Fernandes's pass through the Juve defence, allowing Martins a clear run on goal. Buffon managed to block the ball at Martins's feet, only for it to hit Alex Sandro and ricochet into the net.
At that point, it looked as if Sporting might claim their first win in Italy at their 14th attempt but it turned out to be their only shot on target all evening.
Bayern beat Celtic as Heynckes makes winning European return
First-half goals from Thomas Mueller and Joshua Kimmich put Bayern Munich in the driving seat and Mats Hummels grabbed a third in the 51st minute to round off a dominant 3-0 victory over Celtic, in which the 72-year-old Jupp Heynckes became the oldest coach in the competition's history.
Celtic were no match for the aggressive Bavarians, who were out to get their European campaign back on track after their 3-0 loss to Paris St Germain last month.
That result prompted the sacking of coach Carlo Ancelotti and the return of Heynckes, who led Bayern to the Champions League crown in a treble-winning 2013 season.
Bayern are now second outright in Group B on six points from three matches, three ahead of Celtic and three behind leaders PSG.
Wednesday's results
Benfica 0-1 Manchester United
CSKA Moskva 0-2
Basel Bayern 3-0
Celtic Anderlecht 0-4 Paris St Germain
Chelsea 3-3 Roma
Qarabag 0-0 Atletico
Barcelona 3-1 Olympiacos J
uventus 2-1 Sporting CP
