Mark Aston’s Eagles had an 18-4 lead at half-time, but a hat-trick of tries from Shane Toal completed a stirring recovery from Barrow.
Sheffield opened the scoring on 11 minutes, Ben Blackmore crossing, with Cory Aston converting.
With Barrow’s Brett Carter sin-binned, the visitors increased their lead with tries from Matty Fozzard and Garry Lo - converted by Aston and Simon Brown.
The Raiders cut the deficit, on Carter’s return, when Andy Litherland crossed for an unconverted try before half-time.
But second-half tries from Shane Toal (3), Dan Toal, Ryan Duffy and Joe Bullock earned the hosts victory, despite Lo’s second try late in the game.
Defeat means Sheffield have yet to win in their opening six Championship games, and only kept off bottom spot by Swinton.
Elsewhere, Dewsbury Rams suffered a 36-0 defeat at Leigh Centurions.
The hosts scored 18 points in each half, with tries from Peter Mata’utia (2), Kyle Lovett (2), Harrison Hansen and Ben Crooks. Ben Reynolds kicked four goals, Jack Owens chipping in with two.