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.
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.
"The most important thing is that we're at the head of the group and that won't change so that's good," Klopp said.
"There was some good football but this game should have been put to bed before half-time. We didn't do that, but it's fantastic to win 4-0."
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, AFP reported.
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.
