Liverpool eased Toulouse aside 5-1 to register a third straight Europa League win Thursday, while Brighton beat ailing Dutch giants Ajax for the club's first ever victory in continental competition.
Diogo Jota fired Liverpool in front at Anfield but Thijs Dallinga hauled the French Cup holders level.
Wataru Endo headed in his first goal for the Reds to restore their lead on the half-hour and Darwin Nunez slammed in a third minutes later.
Ryan Gravenberch added a fourth midway through the second half, pouncing on a rebound after Nunez rounded the goalkeeper only to strike the post. Mohamed Salah bagged a fifth in stoppage time.
"Most of the time we were in complete control. We made good goals, nobody got hurt, perfect night," Liverpool boss Jurgen Klopp told TNT Sports.
Liverpool top Group E with nine points and could seal a place in the last 16 with another win in France in two weeks.
They are five points clear of Toulouse and Belgium's Union Saint-Gilloise, who grabbed two late goals to overcome LASK of Austria 2-1.
Brighton claimed a first European win as they beat Ajax 2-0, heaping further misery on the crisis-hit club who parted company with coach Maurice Steijn on Monday just four months into his tenure.
Four-time European champions Ajax are languishing one spot off the foot of the Eredivisie, and fell behind at the Amex Stadium just before half-time to Joao Pedro's tap-in.
Ansu Fati rolled in a second for the hosts early in the second half to leave Roberto De Zerbi's men a point adrift of Group B leaders Marseille.
"The first victory in Europe for Brighton. It's a great day for our fans, our club, our owners. We are very proud to give them this day," De Zerbi told TNT Sports.
Marseille saw off 10-man AEK Athens 3-1 at the Velodrome.
Orbelin Pineda cancelled out Vitinha's opener for Marseille, but a moment of madness from AEK goalkeeper Cican Stankovic cost his team dearly.
Stankovic hit a pass right to Vitinha and then wrestled the Portuguese forward to the ground, conceding a penalty and earning himself a red card.
Amine Harit converted the spot-kick before Jordan Veretout tucked away another penalty for Gennaro Gattuso's side.
West Ham lose in Greece
West Ham's 17-match unbeaten European run came to an end with a 2-1 loss away to Olympiakos.
Kostas Fortounis struck from distance to give the Greek side the lead and Rodinei added a second before half-time with a deflected effort.
Lucas Paqueta volleyed in late consolation for the Hammers, who remain top of Group A on six points from three matches.
"We have to improve our performance. And we must rise to the occasion. I am disappointed by our first half. It was a tough match, but we carry on," said West Ham manager David Moyes.
Freiburg are level with the Hammers after a 3-1 victory over Serbia's Backa Topola.
Rangers relied on a fine display from goalkeeper Jack Butland in a 0-0 draw at Sparta Prague.
The Scottish side are third in Group C, led by Real Betis who won 1-0 away to Aris Limassol thanks to an Ayoze Perez goal.
Bundesliga leaders Bayer Leverkusen thrashed Qarabag 5-1 to stay perfect in Group H and continue their brilliant start to the season under Xabi Alonso.
Roma made it three wins from three in Group G, Edoardo Bove and Romelu Lukaku on target in a 2-0 victory over Slavia Prague.
In the Europa Conference League, in-form Aston Villa eased to a 4-1 win at Dutch high-flyers AZ Alkmaar.
Leon Bailey and Youri Tielemans gave Villa a two-goal lead in the first half against a side who have dropped just two points in the Eredivisie this season.
Ollie Watkins and John McGinn put the game out of reach before Ibrahim Sadiq pulled one back.
