The Eagles are up to second in the table, after registering just one defeat from their opening six matches.
It took the visitors 18 minutes to open the scoring as Quentin Lauulu-Togagae touched down with Dominic Brambani adding the extra before Joe Hirst added to the tally six minutes later.
Lauulu-Togagae, converted by Brambani, and then Menzie Yere went over for Sheffield before the break, although Leigh got their first points when John Duffy scored four minutes after the restart as Martyn Ridyard converted.
Sam Hopkins scored another converted try to give the home side a chance, but Tom Armstrong went over to reassert Sheffield's dominance.
John Duffy went over for a converted score after 64 minutes for Leigh but a minute later Scott Turner scored a converted try, with Misi Taulapapa's late converted effort finishing the scoring.
- Sports & Recreation