Bundesliga leaders Dortmund, who were missing in-form striker Paco Alcacer, delivered the performance of the evening
Barcelona overcame the absence of an injured Lionel Messi to defeat Inter Milan 2-0 in the Champions League on Wednesday, while Borussia Dortmund signalled their intent with a 4-0 demolition of Atletico Madrid.
Mohamed Salah scored twice as Liverpool strolled past Red Star Belgrade, but Paris Saint-Germain needed a superb stoppage-time equaliser from Angel Di Maria to rescue a point at home to Napoli.
Barca collected a third win from three Group B outings as Rafinha, filling in for Messi after the Argentine star fractured his arm at the weekend, volleyed in the opener on 32 minutes at Camp Nou.
Philippe Coutinho rattled the crossbar in the second half before Jordi Alba sealed the points seven minutes from time to leave Barca on the brink of a spot in the last 16.
"We needed to step up given the absence of Leo," Ernesto Valverde said. "It was in the head of us all."
"We have a certain style, then Messi gives us a touch of brilliance that is extraordinary. When he is not there we have to supply it in some other way," he added.
Bundesliga leaders Dortmund, who were missing in-form striker Paco Alcacer, delivered the performance of the evening as they handed last season's Europa League winners Atletico their heaviest defeat under Diego Simeone.
Axel Witsel fired Dortmund ahead shortly before half-time at Signal Iduna Park, with substitute Raphael Guerreiro netting twice in the final quarter-hour either side of a goal by teenage England international Jadon Sancho.
Dortmund top Group A with a maximum nine points, although Atletico still remain favourites to progress alongside them after Thierry Henry's Monaco and Club Brugge drew 1-1 in the other game.
'A draw is not a victory'
Moussa Sylla raised hopes of Monaco ending an 11-match winless streak by opening the scoring just after the half-hour mark in Belgium, but Wesley struck for Brugge to secure a point.
"We are a little less negative than at Strasbourg," said Henry, after a defeat by Strasbourg in his coaching bow on Saturday. "But a draw is a draw, it's not a victory."
At Anfield, Liverpool's front three of Salah, Roberto Firmino and Sadio Mane were all on target as Jurgen Klopp's team swept Serbian champions Red Star aside 4-0.
Firmino broke the deadlock on 20 minutes and Salah struck right before the interval.
The Egyptian then converted a penalty just after the break to become the fastest Liverpool player to 50 goals, achieving the feat in just 65 games.
He missed out on the chance for a hat-trick as he was substituted before Mane missed a second spot-kick, although the Senegalese forward redeemed himself when he stabbed home a Daniel Sturridge cross.
Spurs in deep trouble
Liverpool top Group C by two points from Napoli, who looked on course for an impressive win in France before Di Maria's late heroics in a 2-2 draw at the Parc des Princes.
Carlo Ancelotti's visitors twice led through efforts from Lorenzo Insigne and Dries Mertens, but having levelled once through an own goal by Mario Rui, PSG salvaged a point with Di Maria's marvellous curling 20-yard strike.
"We can improve, it's not possible to make errors because the opposition are very strong," said PSG boss Thomas Tuchel.
"I knew before it would be really complicated, and in my opinion we are not the favourites. This group is really difficult and we can't be surprised."
Tottenham's knockout phase hopes look bleak after conceding a costly late equaliser in a 2-2 draw at PSV Eindhoven.
Hirving Lozano pounced on an error from Toby Alderweireld to put PSV in front on 30 minutes, but Lucas replied for Mauricio Pochettino's side.
Harry Kane nodded in from a Christian Eriksen cross to give Spurs the lead early in the second half, but Hugo Lloris was dismissed for a rash challenge on Lozano after an ill-advised sortie out of his area.
PSV skipper Luuk de Jong hooked a mishit shot past Lloris' replacement Michel Vorm on 87 minutes to leave Spurs five points adrift of second-place Inter in Group B.
"In the end (it was) a draw and (it leaves us) with the minimum possibility to go to the next stage of the Champions League," Pochettino told BT Sport.
Iker Casillas saved a penalty for Porto in a 3-1 win away to 10-man Lokomotiv Moscow as the Portuguese two-time champions seized the initiative in Group D.
Schalke are two points behind Porto following a 0-0 draw away to Galatasaray.