Town needed to win all three of their remaining matches to have any chance of avoiding the drop but their slim hopes were quickly extinguished by the rampant Eagles.
Quentin Laulu-Togagae and Garry Lo scored hat-tricks while Michael Knowles, Duane Straugheir, Matty Fozard, Rhys Jacks and Thibaut Margalet also crossed as Sheffield ran riot to seal Workington’s fate.
Workington’s Cumbrian rivals Whitehaven live to fight another week after a stunning 56-12 victory at play-off hopefuls Dewsbury Rams.
Dave Allen went over twice to give Whitehaven a 10-6 half-time lead and the visitors turned on the style after the break to move to within three points of sixth-placed Oldham with two games remaining.
James Newton, Dion Aiye, Carl Forster (two), Anthony Walker, Ted Chaplow, Ben Davies and Glenn Riley all crossed for Whitehaven in the second half, with Jack Teanby’s second try Dewsbury’s only response.
Bradford Bulls made it five wins out of five in the Kingstone Press Championship Shield despite losing Kurt Haggerty to a red card in the first half of a fiery clash with Swinton Lions.
Ethan Ryan scored a hat-trick, Adam O’Brien went over twice while Jay Pitts, Ben Kavanagh and Dane Chisholm each crossed once as Bradford - who also lost Kris Welham to the sin bin in the second half - dug deep to earn a 46-28 win.
Stuart Littler and Andy Thornley were sin-binned for Swinton, who responded through tries from Macauley Hallett (2), Ben White, Chris Atkin and Mike Butt.
Oldham still require one more victory to confirm their survival after suffering a 32-18 defeat at Halifax.