The Cumbrians never looked back after opening up an 18-0 lead inside 23 minutes thanks to tries from Craig Calvert, Scott McAvoy and Neil Thorman. The Eagles hit back through Mitch Stringer and Menzie Yere but Whitehaven made sure of their fourth win of the season with further tries from James Cameron and Lee Patterson.
Sheffield are now seven points adrift of leaders Halifax, who were 34-16 winners over Doncaster at the Keepmoat Stadium.
The game was over by half-time by which time Halifax centre Steve Tyrer had piled up 16 points with two tries and five goals to help his side into a 34-0 lead.
Rob Worrincy, Sam Barlow, Craig Ashall and Anthony Thackeray were the visitors' other tryscorers, while Chris Spurr, Ben Blakemoor and Brett Waller touched down in the second half for Doncaster.
Batley are up to second thanks to a 30-12 win in the Heavy Woollen derby at Dewsbury, while Leigh made it four wins in a row to keep in touch with the pacesetters, cruising to a 42-22 victory over Workington at Leigh Sports Village.
Featherstone returned to winning ways after back-to-back defeats by demolishing bottom club Swinton 38-18.
Former London Broncos forward Lamont Bryan scored two tries to help Rovers to a 22-6 half-time lead and ex-Wakefield and Bradford prop Matt James touched down twice after the break to finish off the visitors.
James Mendeika, Brad Dwyer and Richie Hawkyard were Swinton's tryscorers.
Former Salford winger Adam Clay scored a last-minute try to complete his hat-trick and help Barrow to a dramatic 20-18 win over York at Craven Park, while Keighley withstood a late onslaught to make it two wins over Easter with a 22-18 win over Hunslet at the South Leeds Stadium.