Liverpool spoiled Chris Wilder's Bramall Lane homecoming to remain hot on the heels of Premier League leaders Arsenal.
Wilder, who led Sheffield United to two promotions in a five-year reign before an unceremonious departure in 2021, received a raucous reaction from the Blades faithful on his return to the dugout.
However, Virgil van Dijk swept home a side-footed volley from Trent Alexander-Arnold's corner to quell the vociferous home support despite Blades appeals he had fouled Anel Ahmedhodzic prior to doing so.
There was also an element of controversy about the Reds' second goal in stoppage time as Darwin Nunez's hefty challenge on Jayden Bogle was deemed fair in the build-up to Dominik Szoboszlai's cool finish.
Liverpool, beaten just once in the league this season when their nine men lost in stoppage time at Tottenham, move back to within two points of the table-topping Gunners.
The Blades, meanwhile, remain bottom, four points from safety, after a 12th loss in 15 league games, although Wilder will take heart from a competitive performance in defeat against the second-placed Reds.