Deputising at centre-back for the injured Virgil van Dijk, Liverpool midfielder Fabinho conceded a 13th-minute penalty for a foul on Oliver McBurnie on the edge of the box, allowing Sander Berge to slot in following a video assistant referee review.
Despite Liverpool facing spirited opposition, Roberto Firmino converted from Sadio Mane’s saved shot four minutes before half-time. Diogo Jota’s header completed the turnaround midway through the second half.
After two league games without victory, including their astonishing 7-2 defeat by Aston Villa, Jurgen Klopp’s side moved level on points at the top of the table with Merseyside rivals Everton, who face Southampton on Sunday at 14:00 GMT.
Jota’s decisive goal arrived two minutes after Mohamed Salah’s fine finish from Trent Alexander-Arnold’s cross was ruled out by VAR for offside, while Salah was denied by the woodwork late on.