With just 10 Premier League matches remaining, Jurgen Klopp's team are just three points adrift of leaders Manchester City, who are next in action on Monday night at Crystal Palace.
Brighton meanwhile have lost their last five Premier League matches on the bounce and have lost some ground on their aim to reach the top 10.
The 2-0 defeat at the Amex Stadium - thanks to goals from Luis Diaz and a penalty from Mo Salah - leaves Brighton in 13th place.
Elsewhere on Saturday, Cristiano Ronaldo grabbed a hat-trick as Manchester United beat Tottenham 3-2 to move back into the top four.
Ivan Toney’s dramatic late double in a 2-0 victory eased Brentford’s relegation fears and deepened Burnley’s.
Earlier today, Chelsea put their troubles aside with a 1-0 win over Newcastle thanks to a winner from Kai Havertz.
Wolves added to Everton's woes with a 1-0 win at Goodison Park - Conor Coad was on target for Bruno Lage's team.
Leeds eased their relegation fears with a 2-1 against Norwich. Rodrigo scored the opener Kenny McLean levelled for the Canaries but Joe Gelhardt netted a vital winner at Elland Road.
Watford gave themselves safety lifeline with a 2-1 win at Southampton and West Ham kept their top four hopes alive thanks a 2-1 triumph over Aston Villa.
Based on the latest odds for relegation following Albion's painful loss, this is where Brighton and Liverpool are now predicted to finish - odds for the title determining where the top sides are expected to end up.
1. 20th - Norwich City (relegated)
Odds for the title: N/A. Odds for relegation: 1-25 (long odds-on favourites for the drop).
2. 19th - Watford (relegated)
Odds for the title: N/A. Odds for relegation: 2-17 (second favourites for the drop).
3. 18th - Burnley (relegated)
Odds for the title: N/A. Odds for relegation: 20-13 (fourth favourites for the drop).
4. 17th - Leeds United (safe)
Odds for the title: N/A. Odds for relegation: 13-9 (third favourites for the drop).