Liverpool secured a 2-0 victory at Bramall Lane, spoiling Chris Wilder’s homecoming as he returned to the dugout at Sheffield United.
Virgil van Dijk opened the scoring with a side-footed volley from Trent Alexander-Arnold’s corner, despite Blades’ appeals for a foul on Anel Ahmedhodzic.
In stoppage time, controversy surrounded Liverpool’s second goal as Darwin Nunez’s challenge on Jayden Bogle was deemed fair in the build-up to Dominik Szoboszlai’s calm finish.
The win keeps Liverpool within two points of Premier League leaders Arsenal, with just one loss in the league this season.
Despite a competitive performance, Sheffield United, under Wilder’s management, remains at the bottom of the table, four points from safety after their 12th loss in 15 league games.