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.