Juventus began their quest for Europa League glory with a 5-0 thrashing of NEC Nijmegen, while Bournemouth secured an impressive victory at Real Sociedad on their European debut on Thursday.
Crystal Palace were 4-0 winners over Lech Poznan, but Celtic suffered another European embarrassment as the Scottish champions were beaten 3-1 at home by Ferencvaros.
Juventus expect to be competing among Europe's elite in the Champions League, but the failure to qualify last season has at least allowed them the chance to end a 30-year wait for a continental trophy.
The Italian giants were far too strong for their Dutch visitors in Turin as Nico Gonzalez, Kerim Alajbegovic and Nick Woltemade, with his first goal since joining on loan from Newcastle, made it 3-0 before half-time.
Zeki Celik and Randal Kolo Muani rounded off the scoring after the break as Juventus made a better start than rivals AC Milan, who lost 2-0 to Benfica in the pick of Wednesday's Europa League action.
Bournemouth had a dream start to their first ever European adventure with a 2-1 win in San Sebastian.
Justin Kluivert opened the scoring before Rayan headed in at the back post to put the Cherries 2-0 up inside 20 minutes.
Blowing leads has been a repeat occurrence for Marco Rose's team in the early weeks of the season.
Rose is yet to taste victory in the Premier League despite Bournemouth going ahead in all four matches so far this season.
"It's a brilliant win in our first European game," said Rose. "It's brilliant for the club and the 2,000 fans from Bournemouth."
Sergio Gomez's attempted cross flew into the far corner to bring Sociedad back into the contest, but this time Bournemouth held on for a memorable victory.
Conference League winners last season, Palace proved far too strong for Lech Poznan to complete a clean sweep of eight victories for the English sides in Champions and Europa League action so far this season.
Yeremy Pino pounced on a calamitous Poznan throw-in to open the scoring at Selhurst Park.
Chris Richards added a second before Jørgen Strand Larsen's penalty made it 3-0 and Eddie Nketiah rounded off the scoring.
Just weeks on from crashing out of the Champions League qualifiers to Austrian side LASK, despite at one point holding a four-goal lead, Celtic's defensive flaws were exposed once more.
Martin O'Neill's side also suffered a chastening 3-0 defeat to local rivals Rangers last weekend and failed to deliver on their manager's promise to respond.
"It's a huge frustration, obviously, but it's also psychologically quite damning as well," said O'Neill.
"Tonight was I think a European lesson for us in many aspects."
Daniel Arzani's sensational strike on his return to Celtic Park capped a fine night for Ferencvaros after a Liam Scales own goal and Kristoffer Zachariassen put the visitors in front.
Besiktas inflicted a fourth consecutive defeat on Marseille with a 4-1 win in Istanbul.
Vaclav Cerny, Micahel Amir Murillo and Ernest Poku struck in the second half after Keyliane Abdallah had cancelled out Ilhan Fakili's opener for the Turkish side.
