Cody Gakpo's double fired Liverpool into the Europa League last 16 as they routed LASK 4-0, while Brighton advanced to the knockout round with a 1-0 win at AEK Athens on Thursday (Nov 30).
Jurgen Klopp's side sealed top spot in Group E thanks to Gakpo's brace and goals from Luis Diaz and Mohamed Salah at Anfield.
Second-placed Toulouse's 0-0 draw against Union Saint-Gilloise in the other group game means Klopp can rest players for his team's last remaining pool stage fixture.
Europa League group winners go through to the last 16 automatically, while the runners-up play in a two-legged knockout round play-off in February against a team who finish third in a Champions League group.
Klopp made nine changes from the side which drew with Premier League champions Manchester City last Saturday, with Salah and Kostas Tsimikas the only players to keep their places.
Rising to meet Joe Gomez's cross, Diaz netted his first goal at Anfield since August as his header raced past LASK keeper Tobias Lawal in the 12th minute.
Having opened the scoring, Diaz helped set up Liverpool's second three minutes later when he picked out Salah, who teed up Gakpo to net from close range.
Salah killed off the out-classed Austrians in the 51st minute, stroking home a penalty for his 13th goal this season after Gakpo was fouled by Lawal.
Dutch forward Gakpo capped the demolition with a fierce strike in stoppage time.
Unlike Liverpool's rich history in continental competition, Brighton are competing in Europe for the first time and the Seagulls' adventure will continue into the New Year thanks to Joao Pedro's winner in Greece.
Damian Szymanski fouled Joao Pedro in the 55th minute and the Brazilian striker picked himself up to slot home the penalty.
AEK's fate was sealed when they were reduced to 10 men in the 85th minute when Mijat Gacinovic earned a second booking for a foul on Joel Veltman.
Roberto De Zerbi's side are second in Group B, one point behind Marseille following the French side's dramatic 4-3 win over 10-man Ajax.
Pierre-Emerick Aubameyang scored a hat-trick for Marseille, including the winner with a penalty three minutes into stoppage time.
In the midst of a wretched season, Ajax had Steven Berghuis sent off in the 63rd minute and were consigned to elimination by their late defeat.
"Who knows how far we can go?" Brighton captain Lewis Dunk said. "We want to win it and you've got to dream big to achieve it.
"We're going to set our sights on reaching the final and winning it."
Soucek strikes late
West Ham moved into the knockout round after a late Tomas Soucek goal saw off Backa Topola 1-0 in Serbia.
Soucek's 89th-minute volley from Maxwel Cornet's cross sealed the victory that put his team top of Group A.
Second-placed Freiburg thrashed Olympiakos 5-0 to join West Ham in the knockout round.
There is a three-way battle for qualification from Group C after third-placed Sparta Prague beat leaders Real Betis 1-0, while second-placed Rangers drew 1-1 with Aris Limassol.
Atalanta wrapped up top spot in Group D after a 1-1 draw against second-placed Sporting Lisbon, who are also through to the knockout round.
Rennes' 3-0 win against Maccabi Haifa took the French team to the top of Group F and into the knockout round, with Villarreal joining them after their 3-2 victory over Panathinaikos.
Slavia Prague's 3-2 win at Sheriff sealed their knockout round place from Group G and Roma also advanced with a 1-1 draw at Servette.
Bayer Leverkusen go through to the last 16 as Group H winners after beating Hacken 2-0.
In the Europa Conference League, crowd troubled marred Aston Villa's 2-1 win against Legia Warsaw as three police officers were injured in clashes with Polish fans.
The game was played with Legia supporters kept out of the stadium following the pre-match violence, which included flares and missiles being hurled at police.