A 6-3 aggregate victory over Hoffenheim, completed on Wednesday, clinched a return to the Champions League but did not appear to take its toll on Liverpool, who were full of energy as they punished a shambolic display from Arsenal.
Arsene Wenger shuffled his back three after last weekend's dismal 1-0 defeat at Stoke City but they were left exposed when Liverpool regained possession high up the pitch and Roberto Firmino headed in the opener.
The visitors were caught out again when Sadio Mane finished off a move that flew from one box to the other and some woeful defending from the bungling Hector Bellerin allowed Mohamed Salah to surge clear to put the result beyond doubt in the second half.
Daniel Sturridge, a 74th-minute replacement for Mane, added gloss to a scoreline that will help overshadow the confusion regarding Simon Mignolet being dropped from the matchday squad as Loris Karius started his first top-flight game since December.
Despite the return of star forward Alexis Sanchez to the starting line-up after an abdominal injury Arsenal were left to mull on another chastening defeat that leaves them with just one win from their first three games.
Danny Welbeck led the Arsenal line ahead of Alexandre Lacazette and wasted a glorious chance to repay Wenger's faith when he lost his footing and fired over under pressure from Joe Gomez.
Salah would have similarly been ruing his finishing in the 10th minute. Emre Can burst into the box via a one-two with Firmino and rolled a cross to the back post for the Egyptian, whose shot along the ground was blocked brilliantly by Petr Cech at full stretch.
Liverpool's high press and counter-attacking caused the visitors consistent problems, Jordan Henderson and Salah both going close before Jurgen Klopp's men added to their tally in trademark fashion.
A length-of-the-pitch break was finished off exquisitely by Mane, who stepped inside Rob Holding on the left and curled a great effort into the far corner.
Wenger replaced Aaron Ramsey – who was making his 300th appearance for the club – with Francis Coquelin for the second half to tighten up Arsenal's porous midfield, but an error from Nacho Monreal led to Salah forcing another save from Cech.
Salah was not so forgiving with his next opportunity, nicking the ball away from Bellerin and sprinting from inside his own half to coolly slot past Cech.
Mane forced Cech into action before making way for Sturridge, who capitalised on slack defending from Laurent Koscielny with a header at the back post for his first goal of the season.
Liverpool were relentless and Cech stayed big to stop Salah adding to their tally in stoppage-time, but it provided Arsenal scant relief as they head into the international break following a stinging loss.
