Even after being reduced to 12 men for the final 40 minutes Sheffield were too strong and organised for Hunslet.
Misi Taulapapa made an impact on the first half with two tries before being shown a red card in the final minute.
The Hawks – who have bolstered their ranks with the capture of former Castleford and Batley player Charlie Martin – were unable to exploit the advantage after the restart to pull back the deficit as a well-organised Eagles out-scored them by three tries to two.
Hunslet’s options had earlier been reduced by the loss of centre Jimmy Kleinhorst following a tackle by Menzie Yere.
Sheffield had the best of a scrappy opening stretching the Hunslet defence with Taulapapa touching down a short chip-kick by Kyle Briggs before a second from Keal Carlile’s flat pass. Pat Walker kicked both the goals
The winger’s involvement ended when he appeared to push his head into the face of Hunslet’s George Flanagan with seconds of the half remaining. Danny Ansell kicked the goal to reduce Sheffield’s advantage to 12-2.
Sheffield’s 12-men took a positive approach and stretched their lead with a try from Quentin Laulu-Togagae but Hunslet seemed in with a chance when Rob Mulhern twisted over.
Again Hunslet’s slack defending cost them as Michael Knowles’ curving run took him in. Flanagan fooled the Eagles defence from a tap penalty with Ansell kicking his third goal before Sheffield found an extra gear in the final minutes.
Yere and Tony Tonks almost forced their way over before Kyle Briggs settled the game sweeping in to give Walker a fourth goal.
Sheffield Eagles: Laulu-Togagae; Turner, Yere, Smeaton, Taulapapa; Briggs, Aston; Battye, Carlile, Tonks, Knowles, Davies, Walker. Subs: Davey, Stringer, Roberts,Thorpe.
Hunslet Hawks: Watson; Finigan, Keinhorst, Maun, Duckworth, Brown, Ansell; Yates, Lee, Brennan, Casey. Walters, Mackay. Subs: Flanagan, Haley, Mulhern, Briscoe.
Referee: Chris Leatherbarrow (RFL).