Diogo Jota's header ensured Liverpool won their first Premier League game without Virgil van Dijk against Sheffield United.
The Reds were forced to come from behind as Sander Berge scored from the penalty spot within the first 15 minutes.
Alisson, who returned to the starting XI after several games out, was unable to keep a clean sheet but made several vital saves to underline his importance.
Roberto Firmino levelled things up shortly before half-time and Jota's effort, just after the hour mark, gave Liverpool the lead.
Andy Robertson and Sadio Mane were amongst the leading lights as the hosts leapt up to second and took advantage of Manchester City's draw at West Ham.
Here are Liverpool's player ratings after a hard fought win at Anfield.
Alisson 7
Brought more solidity back to the team and a couple of good saves
Alexander-Arnold 6
Not quite at his best, but still did well with searching crosses
Fabinho 7
Never a penalty, and didn’t really do much wrong in assured display
Gomez 6
Struggled to contain McBurnie’s power in air, but kept composed
Robertson 8
Outstanding down the left, created so much and always a threat
Henderson 7
Had more work to do in midfield two, and showed he was up to job
Wijnaldum 7
As uncomplicated as ever, controlled tempo of game with passing
Jota 6
Fine header to score, but didn’t get himself in game often enough
Firmino 7
A rare goal, only his second at Anfield this year, but improved
Mane 8
Created two goals, and always a massive handful for visitors
Salah 7
Goal ruled out by fractions, but still maintained Liverpool threat
Subs
Milner N/A
Minamino N/A
