There was a hat-trick for Ferran Torres, the World Cup-winning goalscorer, on his PSG debut in the competition, and two goals for his new teammate Ousmane Dembélé in a 6-1 beating of Slovan Bratislava by the two-time title holders.
At Barcelona, Raphinha scored two more in his rapid-fire start to the season, and Lamine Yamal fired a free kick through Feyenoord's defensive wall in an easy 5-1 win.
It was a typically Arsenal 1-0 win at Napoli with the only goal scored by the English champion's suddenly prolific captain Martin Ødegaard. It's his fourth goal so far after just one in the whole of last season.
All four English clubs won their opening games after Liverpool rallied to beat Atletico Madrid 2-1 with goals by midfielders Dominik Szoboszlai and Alexis Mac Allister. However, Liverpool saw thir record signing Bradley Barcola limp off with an apparent calf injury in the second half.
Unheralded Stuttgart forward Ermedin Demirović got a hat-trick inside 12 first-half minutes in a 3-1 win over Norwegian debutant Viking.
Sporting Lisbon beat Galatasaray 3-1 having also trailed early in the game.
The high rate of goals - 45 through the first 12 games in this Champions League campaign at a rate of 3.75 per game - is well above the average of 3.47 last season. That was itself the highest rate since the 1960s in the old European Cup format.
Raphinha now has eight goals in just five games this season, as if sending a reminder to those who left his name off the Ballon d'Or nominations on Tuesday.
Barcelona got high-class goals from all angles, including from new signings Karim Adeyemi and Gabriel Jesus. Adeyemi found the top corner of Feyenoord's net with a precise curling shot in the 22nd and Jesus came off the bench to glance in a header in the 85th.
Teenage star Yamal fired a free kick left-footed from 20 metres in the 77th that went at waist height between Feyenoord players jumping in the wall.
"He is outstanding," Barcelona coach Hansi Flick said of Yamal, "you can see it every game. He is special."
The 12-minute hat-trick by Stuttgart forward Ermedin Demirović was just the eighth-fastest in the Champions League era, UEFA said.
The Bosnia-Herzegovina forward found his rhythm to strike in the 20th, 26th and 32nd minutes and give Stuttgart a decisive lead against Norwegian newcomers Viking, whose captain Zlatko Tripić had leveled in the 22nd.
PSG's Torres followed suit hours later — in the 31st, 47th and 57th minutes — to make it two trebles after just 12 of the 189-game Champions League season.
Eight hat-tricks were scored last season, including two by Kylian Mbappé in the league phase for Real Madrid, both in away games at Kairat Almaty and Olympiakos.
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